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incrnanskewness

Compute a corrected sample skewness incrementally, ignoring NaN values.

The skewness for a random variable X is defined as

$$\mathop{\mathrm{Skewness}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]$$

For a sample of n values, the sample skewness is

$$b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}$$

where m_3 is the sample third central moment and s is the sample standard deviation.

An alternative definition for the sample skewness which includes an adjustment factor (and is the implemented definition) is

$$G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}$$

Installation

npm install @stdlib/stats-incr-nanskewness

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

incrnanskewness()

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

var accumulator = incrnanskewness();

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated corrected sample skewness. If not provided an input value x, the accumulator function returns the current corrected sample skewness.

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

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.

Examples

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() );

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.