@stdlib/stats-incr-skewness

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incrskewness

Compute a corrected sample skewness incrementally.

The skewness for a random variable X is defined as

-->

For a sample of n values, the sample skewness is

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

Installation

npm install @stdlib/stats-incr-skewness

Usage

var incrskewness = require( '@stdlib/stats-incr-skewness' );

incrskewness()

Returns an accumulator function which incrementally computes a corrected sample skewness.

var accumulator = incrskewness();

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 = incrskewness();

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();
// returns ~0.492

Notes

• Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. 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 randu = require( '@stdlib/random-base-randu' );
var incrskewness = require( '@stdlib/stats-incr-skewness' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrskewness();

// For each simulated datum, update the corrected sample skewness...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );

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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.

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See Also

• @stdlib/stats-incr/kurtosis: compute a corrected sample excess kurtosis incrementally.
• @stdlib/stats-incr/mean: compute an arithmetic mean incrementally.
• @stdlib/stats-incr/stdev: compute a corrected sample standard deviation incrementally.
• @stdlib/stats-incr/summary: compute a statistical summary incrementally.
• @stdlib/stats-incr/variance: compute an unbiased sample variance incrementally.

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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 © 2016-2024. The Stdlib Authors.