npm package: @stdlib/stats-incr-nanskewness
Description: Compute a corrected sample skewness incrementally, ignoring NaN values.
Author: The Stdlib Authors
Latest version: 0.1.1

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# incrnanskewness

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute a [corrected sample skewness][sample-skewness] incrementally, ignoring `NaN` values.

<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."> -->

<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/nanskewness/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."> -->

<!-- <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/nanskewness/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."> -->

<!-- <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/nanskewness/docs/img/equation_adjusted_sample_skewness.svg" alt="Equation for the adjusted sample skewness.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-nanskewness
```

</section>

<section class="usage">

## Usage

```javascript
var incrnanskewness = require( '@stdlib/stats-incr-nanskewness' );
```

#### incrnanskewness()

Returns an accumulator function which incrementally computes a [corrected sample skewness][sample-skewness], ignoring `NaN` values.

```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].

```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
```

</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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-base-uniform' );
var bernoulli = require( '@stdlib/random-base-bernoulli' );
var incrnanskewness = require( '@stdlib/stats-incr-nanskewness' );

// Initialize an accumulator:
var accumulator = incrnanskewness();

// For each simulated datum, update the corrected sample skewness...
var i;
for ( i = 0; i < 100; i++ ) {
    accumulator( ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( 0.0, 100.0 ) );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="references">

</section>

<!-- /.references -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[sample-skewness]: https://en.wikipedia.org/wiki/Skewness

</section>

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