feat: add package stats/incr/nanskewness

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

@@ -0,0 +1,232 @@
+<!--
+
+@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.
+
+-->
+
+# incrnanskewness
+
+> Compute a [corrected sample skewness][sample-skewness] incrementally.
+
+<section class="intro">
+
+The [skewness][sample-skewness] for a random variable `X` is defined as
+
+<!-- <equation class="equation" label="eq:skewness" align="center" raw="\operatorname{Skewness}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]" alt="Equation for skewness."> -->
+
+```math
+\mathop{\mathrm{Skewness}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{Skewness}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]" data-equation="eq:skewness">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/skewness/docs/img/equation_skewness.svg" alt="Equation for skewness.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+For a sample of `n` values, the [sample skewness][sample-skewness] is
+
+<!-- <equation class="equation" label="eq:sample_skewness" align="center" raw="b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}" alt="Equation for the sample skewness."> -->
+
+```math
+b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}" data-equation="eq:sample_skewness">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/skewness/docs/img/equation_sample_skewness.svg" alt="Equation for the sample skewness.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `m_3` is the sample third central moment and `s` is the sample standard deviation.
+
+An alternative definition for the [sample skewness][sample-skewness] which includes an adjustment factor (and is the implemented definition) is
+
+<!-- <equation class="equation" label="eq:adjusted_sample_skewness" align="center" raw="G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}" alt="Equation for the adjusted sample skewness."> -->
+
+```math
+G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}" data-equation="eq:adjusted_sample_skewness">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/skewness/docs/img/equation_adjusted_sample_skewness.svg" alt="Equation for the adjusted sample skewness.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrnanskewness = require( '@stdlib/stats/incr/skewness' );
+```
+
+#### incrnanskewness()
+
+Returns an accumulator `function` which incrementally computes a [corrected sample skewness][sample-skewness].
+
+```javascript
+var accumulator = incrnanskewness();
+```
+
+#### accumulator( \[x] )
+
+If provided an input value `x`, the accumulator function returns an updated [corrected sample skewness][sample-skewness]. If not provided an input value `x`, the accumulator function returns the current [corrected sample skewness][sample-skewness].
+
+<!-- eslint-disable stdlib/doctest -->
+
+```javascript
+var accumulator = incrnanskewness();
+
+var skewness = accumulator();
+// returns null
+
+skewness = accumulator(2.0);
+// returns null
+
+skewness = accumulator(-5.0);
+// returns null
+
+skewness = accumulator(-10.0);
+// returns ~0.492
+
+skewness = accumulator( NaN );
+// returns ~0.492
+
+skewness = accumulator();
+// returns ~0.492
+```
+
+<!-- run-disable -->
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+
+-   For long running accumulations or accumulations of large numbers, care should be taken to prevent overflow.
+
+    </section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+<!-- eslint-disable stdlib/no-redeclare -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanskewness = require( '@stdlib/stats/incr/lib' );
+
+var accumulator;
+var skewness;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanskewness();
+
+// For each simulated datum, update the skewness...
+console.log('\nValue\tSkewness\n');
+for (i = 0; i < 100; i++) {
+    if (randu() < 0.2) {
+        v = NaN;
+    } else {
+        v = randu() * 100.0;
+    }
+    skewness = accumulator(v);
+    console.log( '%d\t%s', v.toFixed(4), (skewness === null) ? 'NaN' : skewness.toFixed(4));
+}
+console.log('\nFinal skewness: %s\n', accumulator());
+```
+
+<!-- run-disable -->
+
+</section>
+
+<!-- /.examples -->
+
+* * *
+
+<section class="references">
+
+## References
+
+-   Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis."
+-   Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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/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/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/stdev`][@stdlib/stats/incr/stdev]</span><span class="delimiter">: </span><span class="description">compute a corrected sample standard deviation 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-skewness]: https://en.wikipedia.org/wiki/Skewness
+[@joanes:1998]: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/skewness]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/skewness
+[@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/stdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/stdev
+[@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/nanskewness/benchmark/benchmark.js

@@ -0,0 +1,69 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2020 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 incrnanskewness = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanskewness();
+		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 = incrnanskewness();
+
+	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();
+});