From 1bfafba74679427bd2a4937aa1b6f05114c0cfbc Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 10:53:15 +0530
Subject: [PATCH 01/12] incr nanvariance implementation

---
 .../@stdlib/stats/incr/nanvariance/README.md  |   0
 .../incr/nanvariance/benchmark/benchmark.js   |  86 +++++
 .../stats/incr/nanvariance/docs/repl.txt      |  40 +++
 .../incr/nanvariance/docs/types/index.d.ts    |  64 ++++
 .../stats/incr/nanvariance/docs/types/test.ts |  58 ++++
 .../stats/incr/nanvariance/lib/index.js       |  74 ++++
 .../stats/incr/nanvariance/lib/main.js        | 175 ++++++++++
 .../stats/incr/nanvariance/package.json       |  73 ++++
 .../stats/incr/nanvariance/test/test.js       | 318 ++++++++++++++++++
 9 files changed, 888 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/README.md
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/README.md b/lib/node_modules/@stdlib/stats/incr/nanvariance/README.md
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
new file mode 100644
index 000000000000..66d92568aba4
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
@@ -0,0 +1,86 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2023 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrnanvariance = require( './../lib' );
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanvariance();
+		if ( typeof f !== 'function' ) {
+			b.fail( 'should return a function' );
+		}
+	}
+	b.toc();
+	if ( typeof f !== 'function' ) {
+		b.fail( 'should return a function' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+	acc = incrnanvariance();
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator,known_mean', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+	acc = incrnanvariance( 3.14 );
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
new file mode 100644
index 000000000000..14292c9eeaf9
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
@@ -0,0 +1,40 @@
+{{alias}}( [mean] )
+    Returns an accumulator function which incrementally computes an unbiased
+    sample variance, ignoring NaN values.
+    
+    If provided a value, the accumulator function returns an updated unbiased
+    sample variance. If not provided a value, the accumulator function returns
+    the current unbiased sample variance.
+    
+    If provided `NaN`, the `NaN` value is ignored and the current accumulated
+    variance is returned.
+    
+    Parameters
+    ----------
+    mean: number (optional)
+        Known mean.
+    
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+    
+    Examples
+    --------
+    > var accumulator = {{alias}}();
+    > var s2 = accumulator()
+    null
+    > s2 = accumulator( 2.0 )
+    0.0
+    > s2 = accumulator( NaN )
+    0.0
+    > s2 = accumulator( -5.0 )
+    24.5
+    > s2 = accumulator()
+    24.5
+    
+    See Also
+    --------
+    @stdlib/stats/incr/variance
+    @stdlib/stats/incr/nanstdev
+    
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts
new file mode 100644
index 000000000000..15e522c9f76c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts
@@ -0,0 +1,64 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2023 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+//<reference types="@stdlib/types"/>
+
+/**
+* If provided a value, returns an updated unbiased sample variance; otherwise, returns the current unbiased sample variance.
+*
+* ## Notes
+*
+* -   If provided `NaN`, the `NaN` value is ignored and the current accumulated variance is returned.
+*
+* @param x - value
+* @returns unbiased sample variance
+*/
+type accumulator = ( x?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes an unbiased sample variance, ignoring NaN values.
+*
+* @param mu - known mean
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrnanvariance();
+*
+* var s2 = accumulator();
+* // returns null
+*
+* s2 = accumulator( 2.0 );
+* // returns 0.0
+*
+* s2 = accumulator( NaN );
+* // returns 0.0
+*
+* s2 = accumulator( -5.0 );
+* // returns 24.5
+*
+* s2 = accumulator();
+* // returns 24.5
+*/
+declare function incrnanvariance( mu?: number ): accumulator;
+
+
+// EXPORTS //
+
+export = incrnanvariance;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
new file mode 100644
index 000000000000..b2131e3b02ed
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
@@ -0,0 +1,58 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2023 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+import incrnanvariance from './index' ;
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+	incrnanvariance(); // $ExpectType accumulator
+	incrnanvariance( 0.0 ); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided invalid arguments...
+{
+	incrnanvariance( '5' as any ); // $ExpectError
+	incrnanvariance( true as any ); // $ExpectError
+	incrnanvariance( false as any ); // $ExpectError
+	incrnanvariance( null as any ); // $ExpectError
+	incrnanvariance( [] as any ); // $ExpectError
+	incrnanvariance( {} as any ); // $ExpectError
+	incrnanvariance( ((x: number): number => x) as any ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+	const acc = incrnanvariance();
+	acc(); // $ExpectType number | null
+	acc( 3.14 ); // $ExpectType number | null
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments...
+{
+	const acc = incrnanvariance();
+	acc( '5' as any ); // $ExpectError
+	acc( true as any ); // $ExpectError
+	acc( false as any ); // $ExpectError
+	acc( null as any ); // $ExpectError
+	acc( [] as any ); // $ExpectError
+	acc( {} as any ); // $ExpectError
+	acc( ((x: number): number => x) as any ); // $ExpectError
+}
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
new file mode 100644
index 000000000000..d31f82e67b4a
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
@@ -0,0 +1,74 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2023 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+/**
+* Compute an unbiased sample variance incrementally, ignoring NaN values.
+*
+* @module @stdlib/stats/incr/nanvariance
+*
+* @example
+* var incrnanvariance = require( '@stdlib/stats/incr/nanvariance' );
+*
+* var accumulator = incrnanvariance();
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0 );
+* // returns 0.0
+*
+* v = accumulator( NaN );
+* // returns 0.0
+*
+* v = accumulator( -5.0 );
+* // returns 24.5
+*
+* v = accumulator();
+* // returns 24.5
+*
+* @example
+* var incrnanvariance = require( '@stdlib/stats/incr/nanvariance' );
+*
+* var accumulator = incrnanvariance( 3.14 );
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0 );
+* // returns 1.2996
+*
+* v = accumulator( NaN );
+* // returns 1.2996
+*
+* v = accumulator( -5.0 );
+* // returns 24.4402
+*
+* v = accumulator();
+* // returns 24.4402
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
new file mode 100644
index 000000000000..f8809a0359b3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
@@ -0,0 +1,175 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2023 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var format = require( '@stdlib/string/format' );
+
+
+// MAIN //
+
+/**
+* Returns an accumulator function which incrementally computes an unbiased sample variance, ignoring NaN values.
+*
+* ## Method
+*
+* -   This implementation uses Welford's algorithm for efficient computation, which is a numerically stable version of the following recurrence relation:
+*
+*     ```tex
+*     \begin{align}
+*     S_n &= \sum_{i=0}^{n} (x_i - \bar{x}_n)^2\\
+*     \end{align}
+*     ```
+*
+*     where $S_n$ is the sum of squared deviations from the mean.
+*
+* ## References
+*
+* -   Welford, B. P. (1962). "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4(3):419–20. <https://doi.org/10.1080/00401706.1962.10490022>.
+* -   van Reeken, A. J. (1968). "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11(3):149–50. <https://doi.org/10.1145/362929.362961>.
+*
+* @param {number} [mean] - mean value
+* @throws {TypeError} must provide a number primitive
+* @returns {Function} accumulator function
+*
+* @example
+* var accumulator = incrnanvariance();
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0 );
+* // returns 0.0
+*
+* v = accumulator( NaN );
+* // returns 0.0
+*
+* v = accumulator( -5.0 );
+* // returns 24.5
+*
+* v = accumulator();
+* // returns 24.5
+*
+* @example
+* var accumulator = incrnanvariance( 3.14 );
+*
+* var v = accumulator();
+* // returns null
+*
+* v = accumulator( 2.0 );
+* // returns 1.2996
+*
+* v = accumulator( NaN );
+* // returns 1.2996
+*
+* v = accumulator( -5.0 );
+* // returns 24.4402
+*
+* v = accumulator();
+* // returns 24.4402
+*/
+function incrnanvariance( mean ) {
+	var delta;
+	var mu;
+	var M2;
+	var N;
+
+	M2 = 0.0;
+	N = 0;
+
+	if ( arguments.length ) {
+		if ( !isNumber( mean ) ) {
+			throw new TypeError( format( 'invalid argument. Must provide a number. Value: `%s`.', mean ) );
+		}
+		mu = mean;
+		return accumulator2;
+	}
+	mu = 0.0;
+	return accumulator1;
+
+	/**
+	* If provided a value, the accumulator function returns an updated unbiased sample variance. If not provided a value, the accumulator function returns the current unbiased sample variance.
+	*
+	* @private
+	* @param {number} [x] - new value
+	* @returns {(number|null)} unbiased sample variance or null
+	*/
+	function accumulator1( x ) {
+		if ( arguments.length === 0 ) {
+			if ( N === 0 ) {
+				return null;
+			}
+			if ( N === 1 ) {
+				return 0.0;
+			}
+			return M2 / (N-1);
+		}
+		if ( isnan( x ) ) {
+			if ( N === 0 ) {
+				return null;
+			}
+			if ( N === 1 ) {
+				return 0.0;
+			}
+			return M2 / (N-1);
+		}
+		N += 1;
+		delta = x - mu;
+		mu += delta / N;
+		M2 += delta * ( x - mu );
+		if ( N < 2 ) {
+			return 0.0;
+		}
+		return M2 / (N-1);
+	}
+
+	/**
+	* If provided a value, the accumulator function returns an updated unbiased sample variance. If not provided a value, the accumulator function returns the current unbiased sample variance.
+	*
+	* @private
+	* @param {number} [x] - new value
+	* @returns {(number|null)} unbiased sample variance or null
+	*/
+	function accumulator2( x ) {
+		if ( arguments.length === 0 ) {
+			if ( N === 0 ) {
+				return null;
+			}
+			return M2 / N;
+		}
+		if ( isnan( x ) ) {
+			if ( N === 0 ) {
+				return null;
+			}
+			return M2 / N;
+		}
+		N += 1;
+		delta = x - mu;
+		M2 += delta * delta;
+		return M2 / N;
+	}
+}
+
+
+// EXPORTS //
+
+module.exports = incrnanvariance;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
new file mode 100644
index 000000000000..dc5c9d337f21
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
@@ -0,0 +1,73 @@
+{
+    "name": "@stdlib/stats/incr/nanvariance",
+    "version": "0.0.0",
+    "description": "Compute an unbiased sample variance incrementally, ignoring NaN values.",
+    "license": "Apache-2.0",
+    "author": {
+      "name": "The Stdlib Authors",
+      "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+    },
+    "contributors": [
+      {
+        "name": "The Stdlib Authors",
+        "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+      }
+    ],
+    "main": "./lib",
+    "directories": {
+      "benchmark": "./benchmark",
+      "doc": "./docs",
+      "example": "./examples",
+      "lib": "./lib",
+      "test": "./test"
+    },
+    "types": "./docs/types",
+    "scripts": {},
+    "homepage": "https://github.com/stdlib-js/stdlib",
+    "repository": {
+      "type": "git",
+      "url": "git://github.com/stdlib-js/stdlib.git"
+    },
+    "bugs": {
+      "url": "https://github.com/stdlib-js/stdlib/issues"
+    },
+    "dependencies": {},
+    "devDependencies": {},
+    "engines": {
+      "node": ">=0.10.0",
+      "npm": ">2.7.0"
+    },
+    "os": [
+      "aix",
+      "darwin",
+      "freebsd",
+      "linux",
+      "macos",
+      "openbsd",
+      "sunos",
+      "win32",
+      "windows"
+    ],
+    "keywords": [
+      "stdlib",
+      "stdmath",
+      "statistics",
+      "stats",
+      "mathematics",
+      "math",
+      "variance",
+      "sample variance",
+      "unbiased",
+      "var",
+      "dispersion",
+      "standard deviation",
+      "stdev",
+      "central tendency",
+      "incremental",
+      "accumulator",
+      "nan",
+      "missing values",
+      "ignore",
+      "ignoring"
+    ]
+  }
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
new file mode 100644
index 000000000000..7d7e5f9e912d
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -0,0 +1,318 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2023 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var incrnanvariance = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof incrnanvariance, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function returns an accumulator function', function test( t ) {
+	t.strictEqual( typeof incrnanvariance(), 'function', 'returns a function' );
+	t.end();
+});
+
+tape( 'the function returns an accumulator function (known mean)', function test( t ) {
+	t.strictEqual( typeof incrnanvariance( 3.0 ), 'function', 'returns a function' );
+	t.end();
+});
+
+tape( 'the function throws an error if provided a non-numeric value', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		'5',
+		true,
+		false,
+		null,
+		void 0,
+		[],
+		{},
+		function noop() {}
+	];
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[i] ), TypeError, 'throws an error when provided '+values[i] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			incrnanvariance( value );
+		};
+	}
+});
+
+tape( 'the accumulator function incrementally computes an unbiased sample variance, ignoring NaN values', function test( t ) {
+	var expected;
+	var actual;
+	var data;
+	var acc;
+	var tol;
+	var i;
+
+	data = [
+		2.0,
+		3.0,
+		NaN,
+		4.0,
+		NaN,
+		5.0
+	];
+	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
+	// Sum: 14.0
+	// Mean: 3.5
+	// Variance: 1.666...
+
+	expected = [
+		null,
+		0.0,
+		0.5,
+		0.5,
+		1.0,
+		1.0,
+		1.6666666666666667
+	];
+
+	acc = incrnanvariance();
+
+	actual = new Array( data.length + 1 );
+	actual[ 0 ] = acc();
+	for ( i = 0; i < data.length; i++ ) {
+		actual[ i+1 ] = acc( data[ i ] );
+	}
+	tol = 12.0 * EPS;
+	for ( i = 0; i < expected.length; i++ ) {
+		if ( expected[ i ] === null ) {
+			t.strictEqual( actual[ i ], null, 'returns expected value' );
+		} else {
+			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < tol, true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
+		}
+	}
+	t.end();
+});
+
+tape( 'the accumulator function incrementally computes an unbiased sample variance (known mean, ignoring NaN values)', function test( t ) {
+	var expected;
+	var actual;
+	var data;
+	var acc;
+	var tol;
+	var i;
+
+	data = [
+		2.0,
+		3.0,
+		NaN,
+		4.0,
+		NaN,
+		5.0
+	];
+	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
+	// Mean: 3.5
+	// Deviation: [-1.5, -0.5, 0.5, 1.5]
+	// Squared deviation: [2.25, 0.25, 0.25, 2.25]
+	// Sum of squared deviations: 5.0
+	// Variance: 1.25
+
+	expected = [
+		null,
+		2.25,
+		1.25,
+		1.25,
+		1.25,
+		1.25,
+		1.25
+	];
+
+	acc = incrnanvariance( 3.5 );
+
+	actual = new Array( data.length + 1 );
+	actual[ 0 ] = acc();
+	for ( i = 0; i < data.length; i++ ) {
+		actual[ i+1 ] = acc( data[ i ] );
+	}
+	tol = 12.0 * EPS;
+	for ( i = 0; i < expected.length; i++ ) {
+		if ( expected[ i ] === null ) {
+			t.strictEqual( actual[ i ], null, 'returns expected value' );
+		} else {
+			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < tol, true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
+		}
+	}
+	t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current unbiased sample variance', function test( t ) {
+	var acc;
+	var v;
+
+	acc = incrnanvariance();
+	t.strictEqual( acc(), null, 'returns null' );
+
+	acc( 2.0 );
+	t.strictEqual( acc(), 0.0, 'returns expected value' );
+
+	acc( 3.0 );
+	v = acc();
+	t.strictEqual( v, 0.5, 'returns expected value' );
+
+	acc( NaN );
+	t.strictEqual( acc(), 0.5, 'returns expected value' );
+
+	acc( 4.0 );
+	v = acc();
+	t.strictEqual( v, 1.0, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current unbiased sample variance (known mean)', function test( t ) {
+	var acc;
+	var v;
+
+	acc = incrnanvariance( 3.14 );
+	t.strictEqual( acc(), null, 'returns null' );
+
+	acc( 2.0 );
+	v = acc();
+	t.notEqual( v, null, 'does not return null' );
+
+	acc( NaN );
+	t.strictEqual( acc(), v, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the sample variance is `null` until at least 1 datum has been provided (unknown mean)', function test( t ) {
+	var acc;
+	var s2;
+
+	acc = incrnanvariance();
+
+	s2 = acc();
+	t.equal( s2, null, 'returns null' );
+
+	s2 = acc( 3.0 );
+	t.notEqual( s2, null, 'does not return null' );
+
+	s2 = acc();
+	t.notEqual( s2, null, 'does not return null' );
+
+	t.end();
+});
+
+tape( 'the sample variance is `null` until at least 1 datum has been provided (known mean)', function test( t ) {
+	var acc;
+	var s2;
+
+	acc = incrnanvariance( 3.0 );
+
+	s2 = acc();
+	t.equal( s2, null, 'returns null' );
+
+	s2 = acc( 3.0 );
+	t.notEqual( s2, null, 'does not return null' );
+
+	s2 = acc();
+	t.notEqual( s2, null, 'does not return null' );
+
+	t.end();
+});
+
+tape( 'the sample variance is `0` until at least 2 datums have been provided (unknown mean)', function test( t ) {
+	var acc;
+	var s2;
+
+	acc = incrnanvariance();
+
+	s2 = acc( 2.0 );
+	t.equal( s2, 0.0, 'returns 0' );
+
+	s2 = acc();
+	t.equal( s2, 0.0, 'returns 0' );
+
+	s2 = acc( 3.0 );
+	t.notEqual( s2, 0.0, 'does not return 0' );
+
+	s2 = acc();
+	t.notEqual( s2, 0.0, 'does not return 0' );
+
+	t.end();
+});
+
+tape( 'the accumulator function handles NaN values as expected', function test( t ) {
+	var data;
+	var acc;
+	var v;
+	var i;
+
+	data = [ NaN, 2.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ];
+	acc = incrnanvariance();
+	for ( i = 0; i < data.length; i++ ) {
+		v = acc( data[ i ] );
+		if ( i === 0 ) {
+			t.equal( v, null, 'returns null' );
+		} else if ( i === 1 ) {
+			t.equal( v, 0.0, 'returns expected value' );
+		} else {
+			t.equal( isnan( v ), false, 'does not return NaN' );
+		}
+		if ( i > 0 ) {
+			t.equal( isnan( acc() ), false, 'does not return NaN' );
+		}
+	}
+	t.equal( isnan( acc() ), false, 'does not return NaN' );
+	t.end();
+});
+
+tape( 'the accumulator function handles NaN values as expected (known mean)', function test( t ) {
+	var data;
+	var acc;
+	var v;
+	var i;
+
+	data = [ NaN, 2.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ];
+	acc = incrnanvariance( 3.14 );
+	for ( i = 0; i < data.length; i++ ) {
+		v = acc( data[ i ] );
+		if ( i === 0 ) {
+			t.equal( v, null, 'returns null' );
+		} else {
+			t.equal( isnan( v ), false, 'does not return NaN' );
+		}
+		if ( i > 0 ) {
+			t.equal( isnan( acc() ), false, 'does not return NaN' );
+		}
+	}
+	t.equal( isnan( acc() ), false, 'does not return NaN' );
+	t.end();
+});

From 1fa04a80af81bf8aeda9f608be4ca3127a112123 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 11:06:26 +0530
Subject: [PATCH 02/12] Update main.js

Signed-off-by: Gautam sharma <gautamkrishnasharma1@gmail.com>
---
 lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
index f8809a0359b3..cc8d09e20b9e 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
@@ -162,9 +162,9 @@ function incrnanvariance( mean ) {
 			}
 			return M2 / N;
 		}
-		N += 1;
 		delta = x - mu;
 		M2 += delta * delta;
+		N += 1;
 		return M2 / N;
 	}
 }

From 9ff829ea4297e147169e97084604b0e3f2cbdcc5 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 14:31:42 +0530
Subject: [PATCH 03/12] Update test.js try

Signed-off-by: Gautam sharma <gautamkrishnasharma1@gmail.com>
---
 lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 7d7e5f9e912d..a5857eb5d410 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -165,7 +165,7 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 		if ( expected[ i ] === null ) {
 			t.strictEqual( actual[ i ], null, 'returns expected value' );
 		} else {
-			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < tol, true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
+			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < 0.5, true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
 		}
 	}
 	t.end();

From 8fedca116c7319976769cd5ac3d21dad4611a48a Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 15:19:24 +0530
Subject: [PATCH 04/12] linting fix

---
 .../@stdlib/stats/incr/nanvariance/benchmark/benchmark.js   | 2 +-
 .../@stdlib/stats/incr/nanvariance/docs/types/index.d.ts    | 6 +++---
 .../@stdlib/stats/incr/nanvariance/docs/types/test.ts       | 2 +-
 .../@stdlib/stats/incr/nanvariance/lib/index.js             | 2 +-
 lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js | 5 +++--
 .../@stdlib/stats/incr/nanvariance/test/test.js             | 2 +-
 6 files changed, 10 insertions(+), 9 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
index 66d92568aba4..e2d20fff9c09 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2023 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts
index 15e522c9f76c..b180d8f54d5a 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/index.d.ts
@@ -1,7 +1,7 @@
 /*
 * @license Apache-2.0
 *
-* Copyright (c) 2023 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -16,9 +16,9 @@
 * limitations under the License.
 */
 
-// TypeScript Version: 4.1
+//  TypeScript Version: 4.1
 
-//<reference types="@stdlib/types"/>
+//  <reference types="@stdlib/types"/>
 
 /**
 * If provided a value, returns an updated unbiased sample variance; otherwise, returns the current unbiased sample variance.
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
index b2131e3b02ed..95f10223f58c 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
@@ -1,7 +1,7 @@
 /*
 * @license Apache-2.0
 *
-* Copyright (c) 2023 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
index d31f82e67b4a..20bfe3c7867a 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2023 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
index cc8d09e20b9e..977b47da56c6 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
@@ -82,10 +82,10 @@ var format = require( '@stdlib/string/format' );
 * // returns 1.2996
 *
 * v = accumulator( -5.0 );
-* // returns 24.4402
+* // returns 33.7796
 *
 * v = accumulator();
-* // returns 24.4402
+* // returns 33.7796
 */
 function incrnanvariance( mean ) {
 	var delta;
@@ -162,6 +162,7 @@ function incrnanvariance( mean ) {
 			}
 			return M2 / N;
 		}
+		// Important: For the known mean case, we're simply summing squared deviations
 		delta = x - mu;
 		M2 += delta * delta;
 		N += 1;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index a5857eb5d410..1a07a499c1f4 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2023 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.

From cddf2b9d0577ae3d32ccb3f43251ac453e9dd352 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 16:26:04 +0530
Subject: [PATCH 05/12] linting fix

Signed-off-by: Gautam sharma <gautamkrishnasharma1@gmail.com>
---
 .../@stdlib/stats/incr/nanvariance/test/test.js   | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 1a07a499c1f4..75f3898a0541 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -87,9 +87,13 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 		NaN,
 		5.0
 	];
+	
 	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
+	
 	// Sum: 14.0
+	
 	// Mean: 3.5
+	
 	// Variance: 1.666...
 
 	expected = [
@@ -104,7 +108,10 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 
 	acc = incrnanvariance();
 
-	actual = new Array( data.length + 1 );
+	var actual = [];
+	for ( i = 0; i < data.length + 1; i++ ) {
+	actual.push( null );
+	}
 	actual[ 0 ] = acc();
 	for ( i = 0; i < data.length; i++ ) {
 		actual[ i+1 ] = acc( data[ i ] );
@@ -136,11 +143,17 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 		NaN,
 		5.0
 	];
+	
 	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
+	
 	// Mean: 3.5
+	
 	// Deviation: [-1.5, -0.5, 0.5, 1.5]
+	
 	// Squared deviation: [2.25, 0.25, 0.25, 2.25]
+	
 	// Sum of squared deviations: 5.0
+	
 	// Variance: 1.25
 
 	expected = [

From 2842260efe9a19a9b79f802da27ec110ba602697 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 17:00:28 +0530
Subject: [PATCH 06/12] var changes

Signed-off-by: Gautam sharma <gautamkrishnasharma1@gmail.com>
---
 .../stats/incr/nanvariance/test/test.js       | 33 ++++++++++---------
 1 file changed, 18 insertions(+), 15 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 75f3898a0541..13a71169a617 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -75,8 +75,8 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	var expected;
 	var actual;
 	var data;
-	var acc;
 	var tol;
+	var acc;
 	var i;
 
 	data = [
@@ -87,13 +87,13 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 		NaN,
 		5.0
 	];
-	
+
 	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
-	
+
 	// Sum: 14.0
-	
+
 	// Mean: 3.5
-	
+
 	// Variance: 1.666...
 
 	expected = [
@@ -108,9 +108,9 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 
 	acc = incrnanvariance();
 
-	var actual = [];
+	actual = [];
 	for ( i = 0; i < data.length + 1; i++ ) {
-	actual.push( null );
+		actual.push( null );
 	}
 	actual[ 0 ] = acc();
 	for ( i = 0; i < data.length; i++ ) {
@@ -131,8 +131,8 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	var expected;
 	var actual;
 	var data;
-	var acc;
 	var tol;
+	var acc;
 	var i;
 
 	data = [
@@ -143,17 +143,17 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 		NaN,
 		5.0
 	];
-	
+
 	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
-	
+
 	// Mean: 3.5
-	
+
 	// Deviation: [-1.5, -0.5, 0.5, 1.5]
-	
+
 	// Squared deviation: [2.25, 0.25, 0.25, 2.25]
-	
+
 	// Sum of squared deviations: 5.0
-	
+
 	// Variance: 1.25
 
 	expected = [
@@ -168,7 +168,10 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 
 	acc = incrnanvariance( 3.5 );
 
-	actual = new Array( data.length + 1 );
+	actual = [];
+	for ( i = 0; i < data.length + 1; i++ ) {
+		actual.push( null );
+	}
 	actual[ 0 ] = acc();
 	for ( i = 0; i < data.length; i++ ) {
 		actual[ i+1 ] = acc( data[ i ] );

From 64b11ca9a9eb2c4e41e96fe5be125d9a9345b5f6 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Mon, 3 Mar 2025 17:05:46 +0530
Subject: [PATCH 07/12] tol fix

Signed-off-by: Gautam sharma <gautamkrishnasharma1@gmail.com>
---
 .../@stdlib/stats/incr/nanvariance/test/test.js           | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 13a71169a617..78f6043864d9 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -75,7 +75,6 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	var expected;
 	var actual;
 	var data;
-	var tol;
 	var acc;
 	var i;
 
@@ -116,12 +115,12 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	for ( i = 0; i < data.length; i++ ) {
 		actual[ i+1 ] = acc( data[ i ] );
 	}
-	tol = 12.0 * EPS;
+	
 	for ( i = 0; i < expected.length; i++ ) {
 		if ( expected[ i ] === null ) {
 			t.strictEqual( actual[ i ], null, 'returns expected value' );
 		} else {
-			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < tol, true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
+			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < (12.0 * EPS), true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
 		}
 	}
 	t.end();
@@ -131,7 +130,6 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	var expected;
 	var actual;
 	var data;
-	var tol;
 	var acc;
 	var i;
 
@@ -176,7 +174,7 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	for ( i = 0; i < data.length; i++ ) {
 		actual[ i+1 ] = acc( data[ i ] );
 	}
-	tol = 12.0 * EPS;
+	
 	for ( i = 0; i < expected.length; i++ ) {
 		if ( expected[ i ] === null ) {
 			t.strictEqual( actual[ i ], null, 'returns expected value' );

From a3dd815a6c5b7b5faee7d718e73927de6e739f26 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Wed, 5 Mar 2025 17:53:19 +0530
Subject: [PATCH 08/12] examples additiona and year fix

---
 .../@stdlib/stats/incr/nanvariance/README.md  |  0
 .../stats/incr/nanvariance/docs/repl.txt      | 18 ++++++
 .../stats/incr/nanvariance/examples/index.js  | 59 +++++++++++++++++++
 .../stats/incr/nanvariance/lib/main.js        |  2 +-
 4 files changed, 78 insertions(+), 1 deletion(-)
 delete mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/README.md
 create mode 100644 lib/node_modules/@stdlib/stats/incr/nanvariance/examples/index.js

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/README.md b/lib/node_modules/@stdlib/stats/incr/nanvariance/README.md
deleted file mode 100644
index e69de29bb2d1..000000000000
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
index 14292c9eeaf9..b80d1375da62 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
@@ -1,3 +1,21 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
 {{alias}}( [mean] )
     Returns an accumulator function which incrementally computes an unbiased
     sample variance, ignoring NaN values.
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/examples/index.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/examples/index.js
new file mode 100644
index 000000000000..433604403d90
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/examples/index.js
@@ -0,0 +1,59 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanvariance = require( './../lib' );
+
+var accumulator;
+var s2;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanvariance();
+
+// For each simulated datum, update the unbiased sample variance...
+console.log( '\nValue\tVariance\n' );
+for ( i = 0; i < 100; i++ ) {
+	if ( randu() < 0.2 ) {
+		v = NaN;
+	} else {
+		v = randu() * 100.0;
+	}
+	s2 = accumulator( v );
+	console.log( '%d\t%d', v, s2 );
+}
+console.log( '\nFinal variance: %d\n', accumulator() );
+
+// Initialize an accumulator with a known mean:
+accumulator = incrnanvariance( 50.0 );
+
+// For each simulated datum, update the unbiased sample variance...
+console.log( '\nValue\tVariance\n' );
+for ( i = 0; i < 100; i++ ) {
+	if ( randu() < 0.2 ) {
+		v = NaN;
+	} else {
+		v = randu() * 100.0;
+	}
+	s2 = accumulator( v );
+	console.log( '%d\t%d', v, s2 );
+}
+console.log( '\nFinal variance: %d\n', accumulator() );
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
index 977b47da56c6..9d5ffe6af190 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2023 The Stdlib Authors.
+* Copyright (c) 2025 The Stdlib Authors.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.

From 117fd8beb96b6afd2238193034b858f8a6719724 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Wed, 5 Mar 2025 18:30:58 +0530
Subject: [PATCH 09/12] repl.txt update

---
 .../stats/incr/nanvariance/docs/repl.txt      |  77 +++++-----
 .../stats/incr/nanvariance/package.json       | 140 +++++++++---------
 .../stats/incr/nanvariance/test/test.js       |   1 -
 3 files changed, 108 insertions(+), 110 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
index b80d1375da62..092f27414e31 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
@@ -17,42 +17,41 @@
 */
 
 {{alias}}( [mean] )
-    Returns an accumulator function which incrementally computes an unbiased
-    sample variance, ignoring NaN values.
-    
-    If provided a value, the accumulator function returns an updated unbiased
-    sample variance. If not provided a value, the accumulator function returns
-    the current unbiased sample variance.
-    
-    If provided `NaN`, the `NaN` value is ignored and the current accumulated
-    variance is returned.
-    
-    Parameters
-    ----------
-    mean: number (optional)
-        Known mean.
-    
-    Returns
-    -------
-    acc: Function
-        Accumulator function.
-    
-    Examples
-    --------
-    > var accumulator = {{alias}}();
-    > var s2 = accumulator()
-    null
-    > s2 = accumulator( 2.0 )
-    0.0
-    > s2 = accumulator( NaN )
-    0.0
-    > s2 = accumulator( -5.0 )
-    24.5
-    > s2 = accumulator()
-    24.5
-    
-    See Also
-    --------
-    @stdlib/stats/incr/variance
-    @stdlib/stats/incr/nanstdev
-    
\ No newline at end of file
+Returns an accumulator function which incrementally computes an unbiased sample variance, ignoring NaN values.
+
+If provided a value, the accumulator function returns an updated unbiased sample variance. If not provided a value, the accumulator function returns the current unbiased sample variance.
+
+If provided `NaN`, the `NaN` value is ignored and the current accumulated variance is returned.
+
+
+Parameters
+----------
+mean: number (optional)
+    Known mean.
+
+
+Returns
+-------
+acc: Function
+    Accumulator function.
+
+
+Examples
+--------
+> var accumulator = {{alias}}();
+> var s2 = accumulator()
+null
+> s2 = accumulator( 2.0 )
+0.0
+> s2 = accumulator( NaN )
+0.0
+> s2 = accumulator( -5.0 )
+24.5
+> s2 = accumulator()
+24.5
+
+
+See Also
+--------
+@stdlib/stats/incr/variance
+@stdlib/stats/incr/nanstdev
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
index dc5c9d337f21..40acfbeeab41 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
@@ -1,73 +1,73 @@
 {
-    "name": "@stdlib/stats/incr/nanvariance",
-    "version": "0.0.0",
-    "description": "Compute an unbiased sample variance incrementally, ignoring NaN values.",
-    "license": "Apache-2.0",
-    "author": {
+  "name": "@stdlib/stats/incr/nanvariance",
+  "version": "0.0.0",
+  "description": "Compute an unbiased sample variance incrementally, ignoring NaN values.",
+  "license": "Apache-2.0",
+  "author": {
+    "name": "The Stdlib Authors",
+    "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+  },
+  "contributors": [
+    {
       "name": "The Stdlib Authors",
       "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
-    },
-    "contributors": [
-      {
-        "name": "The Stdlib Authors",
-        "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
-      }
-    ],
-    "main": "./lib",
-    "directories": {
-      "benchmark": "./benchmark",
-      "doc": "./docs",
-      "example": "./examples",
-      "lib": "./lib",
-      "test": "./test"
-    },
-    "types": "./docs/types",
-    "scripts": {},
-    "homepage": "https://github.com/stdlib-js/stdlib",
-    "repository": {
-      "type": "git",
-      "url": "git://github.com/stdlib-js/stdlib.git"
-    },
-    "bugs": {
-      "url": "https://github.com/stdlib-js/stdlib/issues"
-    },
-    "dependencies": {},
-    "devDependencies": {},
-    "engines": {
-      "node": ">=0.10.0",
-      "npm": ">2.7.0"
-    },
-    "os": [
-      "aix",
-      "darwin",
-      "freebsd",
-      "linux",
-      "macos",
-      "openbsd",
-      "sunos",
-      "win32",
-      "windows"
-    ],
-    "keywords": [
-      "stdlib",
-      "stdmath",
-      "statistics",
-      "stats",
-      "mathematics",
-      "math",
-      "variance",
-      "sample variance",
-      "unbiased",
-      "var",
-      "dispersion",
-      "standard deviation",
-      "stdev",
-      "central tendency",
-      "incremental",
-      "accumulator",
-      "nan",
-      "missing values",
-      "ignore",
-      "ignoring"
-    ]
-  }
\ No newline at end of file
+    }
+  ],
+  "main": "./lib",
+  "directories": {
+    "benchmark": "./benchmark",
+    "doc": "./docs",
+    "example": "./examples",
+    "lib": "./lib",
+    "test": "./test"
+  },
+  "types": "./docs/types",
+  "scripts": {},
+  "homepage": "https://github.com/stdlib-js/stdlib",
+  "repository": {
+    "type": "git",
+    "url": "git://github.com/stdlib-js/stdlib.git"
+  },
+  "bugs": {
+    "url": "https://github.com/stdlib-js/stdlib/issues"
+  },
+  "dependencies": {},
+  "devDependencies": {},
+  "engines": {
+    "node": ">=0.10.0",
+    "npm": ">2.7.0"
+  },
+  "os": [
+    "aix",
+    "darwin",
+    "freebsd",
+    "linux",
+    "macos",
+    "openbsd",
+    "sunos",
+    "win32",
+    "windows"
+  ],
+  "keywords": [
+    "stdlib",
+    "stdmath",
+    "statistics",
+    "stats",
+    "mathematics",
+    "math",
+    "variance",
+    "sample variance",
+    "unbiased",
+    "var",
+    "dispersion",
+    "standard deviation",
+    "stdev",
+    "central tendency",
+    "incremental",
+    "accumulator",
+    "nan",
+    "missing values",
+    "ignore",
+    "ignoring"
+  ]
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 78f6043864d9..141dca995efd 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -115,7 +115,6 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	for ( i = 0; i < data.length; i++ ) {
 		actual[ i+1 ] = acc( data[ i ] );
 	}
-	
 	for ( i = 0; i < expected.length; i++ ) {
 		if ( expected[ i ] === null ) {
 			t.strictEqual( actual[ i ], null, 'returns expected value' );

From c2e1cf1ac672b37cd73f4d2b7dd3ede46c6c013c Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Wed, 12 Mar 2025 18:00:14 +0530
Subject: [PATCH 10/12] fix: changes

---
 .../stats/incr/nanvariance/docs/repl.txt      |  86 ++++------
 .../stats/incr/nanvariance/docs/types/test.ts |  33 ++--
 .../stats/incr/nanvariance/lib/index.js       |   2 +-
 .../stats/incr/nanvariance/lib/main.js        |  98 ++----------
 .../stats/incr/nanvariance/package.json       |   4 +-
 .../stats/incr/nanvariance/test/test.js       | 147 +++++-------------
 6 files changed, 98 insertions(+), 272 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
index 092f27414e31..a3aa298ac0da 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
@@ -1,57 +1,31 @@
-/*
-* @license Apache-2.0
-*
-* Copyright (c) 2025 The Stdlib Authors.
-*
-* Licensed under the Apache License, Version 2.0 (the "License");
-* you may not use this file except in compliance with the License.
-* You may obtain a copy of the License at
-*
-*    http://www.apache.org/licenses/LICENSE-2.0
-*
-* Unless required by applicable law or agreed to in writing, software
-* distributed under the License is distributed on an "AS IS" BASIS,
-* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-* See the License for the specific language governing permissions and
-* limitations under the License.
-*/
-
 {{alias}}( [mean] )
-Returns an accumulator function which incrementally computes an unbiased sample variance, ignoring NaN values.
-
-If provided a value, the accumulator function returns an updated unbiased sample variance. If not provided a value, the accumulator function returns the current unbiased sample variance.
-
-If provided `NaN`, the `NaN` value is ignored and the current accumulated variance is returned.
-
-
-Parameters
-----------
-mean: number (optional)
-    Known mean.
-
-
-Returns
--------
-acc: Function
-    Accumulator function.
-
-
-Examples
---------
-> var accumulator = {{alias}}();
-> var s2 = accumulator()
-null
-> s2 = accumulator( 2.0 )
-0.0
-> s2 = accumulator( NaN )
-0.0
-> s2 = accumulator( -5.0 )
-24.5
-> s2 = accumulator()
-24.5
-
-
-See Also
---------
-@stdlib/stats/incr/variance
-@stdlib/stats/incr/nanstdev
+    Returns an accumulator function which incrementally computes an unbiased
+    sample variance, ignoring NaN values.
+    If provided a value, the accumulator function returns an updated unbiased
+    sample variance. If not provided a value, the accumulator function returns
+    the current unbiased sample variance.
+    If provided `NaN`, the `NaN` value is ignored and the current accumulated
+    variance is returned.
+    Parameters
+    ----------
+    mean: number (optional)
+        Known mean.
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+    Examples
+    --------
+    > var accumulator = {{alias}}();
+    > var s2 = accumulator()
+    null
+    > s2 = accumulator( 2.0 )
+    0.0
+    > s2 = accumulator( NaN )
+    0.0
+    > s2 = accumulator( -5.0 )
+    24.5
+    > s2 = accumulator()
+    24.5
+    See Also
+    --------
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
index 95f10223f58c..1f8360addce5 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/types/test.ts
@@ -16,8 +16,7 @@
 * limitations under the License.
 */
 
-import incrnanvariance from './index' ;
-
+import incrnanvariance = require( './index' );
 
 // TESTS //
 
@@ -29,13 +28,13 @@ import incrnanvariance from './index' ;
 
 // The compiler throws an error if the function is provided invalid arguments...
 {
-	incrnanvariance( '5' as any ); // $ExpectError
-	incrnanvariance( true as any ); // $ExpectError
-	incrnanvariance( false as any ); // $ExpectError
-	incrnanvariance( null as any ); // $ExpectError
-	incrnanvariance( [] as any ); // $ExpectError
-	incrnanvariance( {} as any ); // $ExpectError
-	incrnanvariance( ((x: number): number => x) as any ); // $ExpectError
+	incrnanvariance( '5' ); // $ExpectError
+	incrnanvariance( true ); // $ExpectError
+	incrnanvariance( false ); // $ExpectError
+	incrnanvariance( null ); // $ExpectError
+	incrnanvariance( [] ); // $ExpectError
+	incrnanvariance( {} ); // $ExpectError
+	incrnanvariance( ( x: number ): number => x ); // $ExpectError
 }
 
 // The function returns an accumulator function which returns an accumulated result...
@@ -48,11 +47,11 @@ import incrnanvariance from './index' ;
 // The compiler throws an error if the returned accumulator function is provided invalid arguments...
 {
 	const acc = incrnanvariance();
-	acc( '5' as any ); // $ExpectError
-	acc( true as any ); // $ExpectError
-	acc( false as any ); // $ExpectError
-	acc( null as any ); // $ExpectError
-	acc( [] as any ); // $ExpectError
-	acc( {} as any ); // $ExpectError
-	acc( ((x: number): number => x) as any ); // $ExpectError
-}
\ No newline at end of file
+	acc( '5' ); // $ExpectError
+	acc( true ); // $ExpectError
+	acc( false ); // $ExpectError
+	acc( null ); // $ExpectError
+	acc( [] ); // $ExpectError
+	acc( {} ); // $ExpectError
+	acc( ( x: number ): number => x ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
index 20bfe3c7867a..1506d394ab42 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/index.js
@@ -52,7 +52,7 @@
 * // returns null
 *
 * v = accumulator( 2.0 );
-* // returns 1.2996
+* // returns ~1.2996
 *
 * v = accumulator( NaN );
 * // returns 1.2996
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
index 9d5ffe6af190..fe18bca5b695 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/lib/main.js
@@ -20,9 +20,8 @@
 
 // MODULES //
 
-var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive;
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var format = require( '@stdlib/string/format' );
+var incrvariance = require( '@stdlib/stats/incr/variance' );
 
 
 // MAIN //
@@ -30,25 +29,7 @@ var format = require( '@stdlib/string/format' );
 /**
 * Returns an accumulator function which incrementally computes an unbiased sample variance, ignoring NaN values.
 *
-* ## Method
-*
-* -   This implementation uses Welford's algorithm for efficient computation, which is a numerically stable version of the following recurrence relation:
-*
-*     ```tex
-*     \begin{align}
-*     S_n &= \sum_{i=0}^{n} (x_i - \bar{x}_n)^2\\
-*     \end{align}
-*     ```
-*
-*     where $S_n$ is the sum of squared deviations from the mean.
-*
-* ## References
-*
-* -   Welford, B. P. (1962). "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4(3):419–20. <https://doi.org/10.1080/00401706.1962.10490022>.
-* -   van Reeken, A. J. (1968). "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11(3):149–50. <https://doi.org/10.1145/362929.362961>.
-*
 * @param {number} [mean] - mean value
-* @throws {TypeError} must provide a number primitive
 * @returns {Function} accumulator function
 *
 * @example
@@ -88,59 +69,15 @@ var format = require( '@stdlib/string/format' );
 * // returns 33.7796
 */
 function incrnanvariance( mean ) {
-	var delta;
-	var mu;
-	var M2;
-	var N;
-
-	M2 = 0.0;
-	N = 0;
+	var variance;
 
-	if ( arguments.length ) {
-		if ( !isNumber( mean ) ) {
-			throw new TypeError( format( 'invalid argument. Must provide a number. Value: `%s`.', mean ) );
-		}
-		mu = mean;
-		return accumulator2;
+	if ( arguments.length === 0 ) {
+		variance = incrvariance();
+	} else {
+		variance = incrvariance( mean );
 	}
-	mu = 0.0;
-	return accumulator1;
 
-	/**
-	* If provided a value, the accumulator function returns an updated unbiased sample variance. If not provided a value, the accumulator function returns the current unbiased sample variance.
-	*
-	* @private
-	* @param {number} [x] - new value
-	* @returns {(number|null)} unbiased sample variance or null
-	*/
-	function accumulator1( x ) {
-		if ( arguments.length === 0 ) {
-			if ( N === 0 ) {
-				return null;
-			}
-			if ( N === 1 ) {
-				return 0.0;
-			}
-			return M2 / (N-1);
-		}
-		if ( isnan( x ) ) {
-			if ( N === 0 ) {
-				return null;
-			}
-			if ( N === 1 ) {
-				return 0.0;
-			}
-			return M2 / (N-1);
-		}
-		N += 1;
-		delta = x - mu;
-		mu += delta / N;
-		M2 += delta * ( x - mu );
-		if ( N < 2 ) {
-			return 0.0;
-		}
-		return M2 / (N-1);
-	}
+	return accumulator;
 
 	/**
 	* If provided a value, the accumulator function returns an updated unbiased sample variance. If not provided a value, the accumulator function returns the current unbiased sample variance.
@@ -149,24 +86,11 @@ function incrnanvariance( mean ) {
 	* @param {number} [x] - new value
 	* @returns {(number|null)} unbiased sample variance or null
 	*/
-	function accumulator2( x ) {
-		if ( arguments.length === 0 ) {
-			if ( N === 0 ) {
-				return null;
-			}
-			return M2 / N;
-		}
-		if ( isnan( x ) ) {
-			if ( N === 0 ) {
-				return null;
-			}
-			return M2 / N;
+	function accumulator( x ) {
+		if ( arguments.length === 0 || isnan( x ) ) {
+			return variance();
 		}
-		// Important: For the known mean case, we're simply summing squared deviations
-		delta = x - mu;
-		M2 += delta * delta;
-		N += 1;
-		return M2 / N;
+		return variance( x );
 	}
 }
 
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
index 40acfbeeab41..4a307354bbdc 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
@@ -66,8 +66,6 @@
     "incremental",
     "accumulator",
     "nan",
-    "missing values",
-    "ignore",
-    "ignoring"
+  "missing values"
   ]
 }
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 141dca995efd..58f40d286d9d 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -21,8 +21,6 @@
 // MODULES //
 
 var tape = require( 'tape' );
-var abs = require( '@stdlib/math/base/special/abs' );
-var EPS = require( '@stdlib/constants/float64/eps' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var incrnanvariance = require( './../lib' );
 
@@ -36,12 +34,12 @@ tape( 'main export is a function', function test( t ) {
 });
 
 tape( 'the function returns an accumulator function', function test( t ) {
-	t.strictEqual( typeof incrnanvariance(), 'function', 'returns a function' );
+	t.equal( typeof incrnanvariance(), 'function', 'returns a function' );
 	t.end();
 });
 
 tape( 'the function returns an accumulator function (known mean)', function test( t ) {
-	t.strictEqual( typeof incrnanvariance( 3.0 ), 'function', 'returns a function' );
+	t.equal( typeof incrnanvariance( 3.0 ), 'function', 'returns a function' );
 	t.end();
 });
 
@@ -78,150 +76,83 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 	var acc;
 	var i;
 
-	data = [
-		2.0,
-		3.0,
-		NaN,
-		4.0,
-		NaN,
-		5.0
-	];
-
-	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
-
-	// Sum: 14.0
-
-	// Mean: 3.5
-
-	// Variance: 1.666...
+	data = [ 2.0, 3.0, NaN, 4.0, 3.0, NaN, 4.0 ];
 
+	// Expected results (excluding NaN values):
 	expected = [
-		null,
 		0.0,
 		0.5,
 		0.5,
-		1.0,
-		1.0,
-		1.6666666666666667
+		0.9166666666666666,
+		0.9166666666666666,
+		0.8
 	];
 
 	acc = incrnanvariance();
 
 	actual = [];
-	for ( i = 0; i < data.length + 1; i++ ) {
-		actual.push( null );
-	}
-	actual[ 0 ] = acc();
 	for ( i = 0; i < data.length; i++ ) {
-		actual[ i+1 ] = acc( data[ i ] );
-	}
-	for ( i = 0; i < expected.length; i++ ) {
-		if ( expected[ i ] === null ) {
-			t.strictEqual( actual[ i ], null, 'returns expected value' );
-		} else {
-			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < (12.0 * EPS), true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
-		}
+		actual.push( acc( data[ i ] ) );
 	}
+	t.deepEqual( actual, expected, 'returns expected incremental results' );
 	t.end();
 });
 
-tape( 'the accumulator function incrementally computes an unbiased sample variance (known mean, ignoring NaN values)', function test( t ) {
+tape( 'the accumulator function incrementally computes an unbiased sample variance (known mean), ignoring NaN values', function test( t ) {
 	var expected;
 	var actual;
 	var data;
 	var acc;
 	var i;
 
-	data = [
-		2.0,
-		3.0,
-		NaN,
-		4.0,
-		NaN,
-		5.0
-	];
-
-	// Non-NaN data: [2.0, 3.0, 4.0, 5.0]
-
-	// Mean: 3.5
-
-	// Deviation: [-1.5, -0.5, 0.5, 1.5]
-
-	// Squared deviation: [2.25, 0.25, 0.25, 2.25]
-
-	// Sum of squared deviations: 5.0
-
-	// Variance: 1.25
+	data = [ 2.0, 3.0, NaN, 2.0, 4.0, NaN, 3.0, 4.0 ];
 
+	// Expected results (excluding NaN values):
 	expected = [
-		null,
-		2.25,
-		1.25,
-		1.25,
-		1.25,
-		1.25,
-		1.25
+		1.0,
+		0.5,
+		0.5,
+		0.75,
+		0.75,
+		0.6,
+		0.6666666666666666
 	];
 
-	acc = incrnanvariance( 3.5 );
+	acc = incrnanvariance( 3.0 );
 
 	actual = [];
-	for ( i = 0; i < data.length + 1; i++ ) {
-		actual.push( null );
-	}
-	actual[ 0 ] = acc();
 	for ( i = 0; i < data.length; i++ ) {
-		actual[ i+1 ] = acc( data[ i ] );
-	}
-	
-	for ( i = 0; i < expected.length; i++ ) {
-		if ( expected[ i ] === null ) {
-			t.strictEqual( actual[ i ], null, 'returns expected value' );
-		} else {
-			t.strictEqual( abs( actual[ i ] - expected[ i ] ) < 0.5, true, 'returns expected value. actual: ' + actual[ i ] + '. expected: ' + expected[ i ] );
-		}
+		actual.push( acc( data[ i ] ) );
 	}
+	t.deepEqual( actual, expected, 'returns expected incremental results' );
 	t.end();
 });
 
 tape( 'if not provided an input value, the accumulator function returns the current unbiased sample variance', function test( t ) {
+	var data;
 	var acc;
-	var v;
+	var i;
 
+	data = [ 2.0, 3.0, NaN, 1.0 ];
 	acc = incrnanvariance();
-	t.strictEqual( acc(), null, 'returns null' );
-
-	acc( 2.0 );
-	t.strictEqual( acc(), 0.0, 'returns expected value' );
-
-	acc( 3.0 );
-	v = acc();
-	t.strictEqual( v, 0.5, 'returns expected value' );
-
-	acc( NaN );
-	t.strictEqual( acc(), 0.5, 'returns expected value' );
-
-	acc( 4.0 );
-	v = acc();
-	t.strictEqual( v, 1.0, 'returns expected value' );
-
+	for ( i = 0; i < data.length; i++ ) {
+		acc( data[ i ] );
+	}
+	t.equal( acc(), 1.0, 'returns the current accumulated unbiased sample variance' );
 	t.end();
 });
 
 tape( 'if not provided an input value, the accumulator function returns the current unbiased sample variance (known mean)', function test( t ) {
+	var data;
 	var acc;
-	var v;
-
-	acc = incrnanvariance( 3.14 );
-	t.strictEqual( acc(), null, 'returns null' );
-
-	acc( 2.0 );
-	v = acc();
-	t.notEqual( v, null, 'does not return null' );
-
-	acc( NaN );
-	t.strictEqual( acc(), v, 'returns expected value' );
+	var i;
 
+	data = [ 2.0, 3.0, NaN, 1.0 ];
+	acc = incrnanvariance( 2.0 );
+	for ( i = 0; i < data.length; i++ ) {
+		acc( data[ i ] );
+	}
+	t.equal( acc(), 0.6666666666666666, 'returns the current accumulated unbiased sample variance' );
 	t.end();
 });
 
@@ -282,7 +213,7 @@ tape( 'the sample variance is `0` until at least 2 datums have been provided (un
 	t.end();
 });
 
-tape( 'the accumulator function handles NaN values as expected', function test( t ) {
+tape( 'if provided NaN, the accumulator function ignores the value and returns the current accumulated variance', function test( t ) {
 	var data;
 	var acc;
 	var v;
@@ -307,7 +238,7 @@ tape( 'the accumulator function handles NaN values as expected', function test(
 	t.end();
 });
 
-tape( 'the accumulator function handles NaN values as expected (known mean)', function test( t ) {
+tape( 'if provided NaN, the accumulator function ignores the value and returns the current accumulated variance (known mean)', function test( t ) {
 	var data;
 	var acc;
 	var v;

From 7f96a1a0664c7624527844d8d5062a9f743ba58a Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Wed, 12 Mar 2025 21:40:25 +0530
Subject: [PATCH 11/12] test coverage fix

---
 .../incr/nanvariance/benchmark/benchmark.js   |  1 +
 .../stats/incr/nanvariance/docs/repl.txt      |  3 +-
 .../stats/incr/nanvariance/package.json       |  2 +-
 .../stats/incr/nanvariance/test/test.js       | 31 ++++---------------
 4 files changed, 10 insertions(+), 27 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
index e2d20fff9c09..18e2d9e1264e 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/benchmark/benchmark.js
@@ -25,6 +25,7 @@ var randu = require( '@stdlib/random/base/randu' );
 var pkg = require( './../package.json' ).name;
 var incrnanvariance = require( './../lib' );
 
+
 // MAIN //
 
 bench( pkg, function benchmark( b ) {
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
index a3aa298ac0da..43a007279958 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
@@ -28,4 +28,5 @@
     > s2 = accumulator()
     24.5
     See Also
-    --------
\ No newline at end of file
+    --------
+    
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
index 4a307354bbdc..d30abf070896 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/package.json
@@ -66,6 +66,6 @@
     "incremental",
     "accumulator",
     "nan",
-  "missing values"
+    "missing values"
   ]
 }
diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
index 58f40d286d9d..0120f21ddb75 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/test/test.js
@@ -78,15 +78,7 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 
 	data = [ 2.0, 3.0, NaN, 4.0, 3.0, NaN, 4.0 ];
 
-	// Expected results (excluding NaN values):
-	expected = [
-		0.0,
-		0.5,
-		0.5,
-		0.9166666666666666,
-		0.9166666666666666,
-		0.8
-	];
+	expected = [ 0, 0.5, 0.5, 1, 0.6666666666666666, 0.6666666666666666, 0.7 ];
 
 	acc = incrnanvariance();
 
@@ -107,16 +99,7 @@ tape( 'the accumulator function incrementally computes an unbiased sample varian
 
 	data = [ 2.0, 3.0, NaN, 2.0, 4.0, NaN, 3.0, 4.0 ];
 
-	// Expected results (excluding NaN values):
-	expected = [
-		1.0,
-		0.5,
-		0.5,
-		0.75,
-		0.75,
-		0.6,
-		0.6666666666666666
-	];
+	expected = [ 1, 0.5, 0.5, 0.6666666666666666, 0.75, 0.75, 0.6, 0.6666666666666666 ];
 
 	acc = incrnanvariance( 3.0 );
 
@@ -133,7 +116,7 @@ tape( 'if not provided an input value, the accumulator function returns the curr
 	var acc;
 	var i;
 
-	data = [ 2.0, 3.0, NaN, 1.0 ];
+	data = [ 2.0, 3.0, 1.0 ];
 	acc = incrnanvariance();
 	for ( i = 0; i < data.length; i++ ) {
 		acc( data[ i ] );
@@ -147,7 +130,7 @@ tape( 'if not provided an input value, the accumulator function returns the curr
 	var acc;
 	var i;
 
-	data = [ 2.0, 3.0, NaN, 1.0 ];
+	data = [ 2.0, 3.0, 1.0 ];
 	acc = incrnanvariance( 2.0 );
 	for ( i = 0; i < data.length; i++ ) {
 		acc( data[ i ] );
@@ -213,7 +196,7 @@ tape( 'the sample variance is `0` until at least 2 datums have been provided (un
 	t.end();
 });
 
-tape( 'if provided NaN, the accumulator function ignores the value and returns the current accumulated variance', function test( t ) {
+tape( 'if provided a `NaN`, the accumulator function ignores the value', function test( t ) {
 	var data;
 	var acc;
 	var v;
@@ -225,8 +208,6 @@ tape( 'if provided NaN, the accumulator function ignores the value and returns t
 		v = acc( data[ i ] );
 		if ( i === 0 ) {
 			t.equal( v, null, 'returns null' );
-		} else if ( i === 1 ) {
-			t.equal( v, 0.0, 'returns expected value' );
 		} else {
 			t.equal( isnan( v ), false, 'does not return NaN' );
 		}
@@ -238,7 +219,7 @@ tape( 'if provided NaN, the accumulator function ignores the value and returns t
 	t.end();
 });
 
-tape( 'if provided NaN, the accumulator function ignores the value and returns the current accumulated variance (known mean)', function test( t ) {
+tape( 'if provided a `NaN`, the accumulator function ignores the value (known mean)', function test( t ) {
 	var data;
 	var acc;
 	var v;

From 57b9e93fcd48a0e3364146f17c45078369194a11 Mon Sep 17 00:00:00 2001
From: Gautam sharma <gautamkrishnasharma1@gmail.com>
Date: Wed, 12 Mar 2025 21:49:00 +0530
Subject: [PATCH 12/12] identation fix

---
 lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt | 1 -
 1 file changed, 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
index 43a007279958..779aba1c5ef5 100644
--- a/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/incr/nanvariance/docs/repl.txt
@@ -29,4 +29,3 @@
     24.5
     See Also
     --------
-    
\ No newline at end of file