feat: add incremental corrected sample standard deviation function that ignores NaN values

Author: Girish-Garg

lib/node_modules/@stdlib/stats/incr/nanapcorr/lib/main.js

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2018 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.
+
+-->
+
+# incrstdev
+
+> Compute a [corrected sample standard deviation][sample-stdev] incrementally.
+
+<section class="intro">
+
+The [corrected sample standard deviation][sample-stdev] is defined as
+
+<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}" alt="Equation for the corrected sample standard deviation."> -->
+
+```math
+s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}" data-equation="eq:corrected_sample_standard_deviation">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/stdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for the corrected sample standard deviation.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrstdev = require( '@stdlib/stats/incr/nanstdev' );
+```
+
+#### incrstdev( \[mean] )
+
+Returns an accumulator `function` which incrementally computes a [corrected sample standard deviation][sample-stdev].
+
+```javascript
+var accumulator = incrnanstdev();
+```
+
+If the mean is already known, provide a `mean` argument.
+
+```javascript
+var accumulator = incrnanstdev( 3.0 );
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated [corrected sample standard deviation][sample-stdev]. If not provided an input value `x`, the accumulator function returns the current [corrected sample standard deviation][sample-stdev].
+
+```javascript
+var accumulator = incrnanstdev();
+
+var s = accumulator( 2.0 );
+// returns 0.0
+
+s = accumulator( 1.0 ); // => sqrt(((2-1.5)^2+(1-1.5)^2) / (2-1))
+// returns ~0.7071
+
+s = accumulator( NaN ); // Ignored
+// return ~0.7071
+
+s = accumulator( 3.0 ); // => sqrt(((2-2)^2+(1-2)^2+(3-2)^2) / (3-1))
+// returns 1.0
+
+s = accumulator();
+// returns 1.0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, It will be Ignored Automatically without any errors but  you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanstdev = require( './../lib' );
+
+var accumulator;
+var s;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanstdev();
+
+// For each simulated datum, update the corrected sample standard deviation...
+for ( i = 0; i < 100; i++ ) {
+    v = randu() * 100.0;
+
+    // Introduce NaN values randomly to test the accumulator
+    if ( randu() < 0.1 ) { // 10% chance to insert NaN
+        v = NaN;
+    }
+
+    s = accumulator( v );
+}
+console.log( '\nFinal standard deviation: %d\n', accumulator() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/stats/incr/kurtosis`][@stdlib/stats/incr/kurtosis]</span><span class="delimiter">: </span><span class="description">compute a corrected sample excess kurtosis incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/mean`][@stdlib/stats/incr/mean]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/mstdev`][@stdlib/stats/incr/mstdev]</span><span class="delimiter">: </span><span class="description">compute a moving corrected sample standard deviation incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/skewness`][@stdlib/stats/incr/skewness]</span><span class="delimiter">: </span><span class="description">compute a corrected sample skewness incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/summary`][@stdlib/stats/incr/summary]</span><span class="delimiter">: </span><span class="description">compute a statistical summary incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/variance`][@stdlib/stats/incr/variance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample variance incrementally.</span>
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[sample-stdev]: https://en.wikipedia.org/wiki/Standard_deviation
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/kurtosis]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/kurtosis
+
+[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mean
+
+[@stdlib/stats/incr/mstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mstdev
+
+[@stdlib/stats/incr/skewness]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/skewness
+
+[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/summary
+
+[@stdlib/stats/incr/variance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/variance
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/nanstdev/README.md

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 incrnanstdev = require( './../lib' );
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanstdev();
+		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 = incrnanstdev();
+
+	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 = incrnanstdev( 3.0 );
+
+	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();
+});

lib/node_modules/@stdlib/stats/incr/nanstdev/benchmark/benchmark.js

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+
+{{alias}}( [mean] )
+    Returns an accumulator function which incrementally computes a corrected
+    sample standard deviation, ignoring `NaN` values.
+
+    If provided a value, the accumulator function returns an updated corrected
+    sample standard deviation. If not provided a value, the accumulator function
+    returns the current corrected sample standard deviation.
+
+    If provided `NaN` or a value which, when used in computations, results in
+    `NaN`, the value is ignored and does not affect future calculations.
+
+    Parameters
+    ----------
+    mean: number (optional)
+        Known mean.
+
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+
+    Examples
+    --------
+    > var accumulator = {{alias}}();
+    > var s = accumulator()
+    null
+    > s = accumulator( 2.0 )
+    0.0
+    > s = accumulator( NaN )
+    0.0
+    > s = accumulator( -5.0 )
+    ~4.95
+    > s = accumulator()
+    ~4.95
+
+    See Also
+    --------

lib/node_modules/@stdlib/stats/incr/nanstdev/docs/img/equation_corrected_sample_standard_deviation.svg

@@ -0,0 +1,64 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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 corrected sample standard deviation; otherwise, returns the current corrected sample standard deviation.
+*
+* ## Notes
+*
+* -   If provided `NaN` or a value which, when used in computations, the value is ignored and does not affect future calculations.
+*
+* @param x - value
+* @returns corrected sample standard deviation
+*/
+type accumulator = ( x?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes a corrected sample standard deviation.
+*
+* @param mu - known mean
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrstdev();
+*
+* var s = accumulator();
+* // returns null
+*
+* s = accumulator( 2.0 );
+* // returns 0.0
+*
+* s = accumulator( NaN );
+* // returns 0.0
+*
+* s = accumulator( -5.0 );
+* // returns ~4.95
+*
+* s = accumulator();
+* // returns ~4.95
+*/
+declare function incrnanstdev( mu?: number ): accumulator;
+
+
+// EXPORTS //
+
+export = incrnanstdev;