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@stdlib/stats-base-dists-chisquare-mgf

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@stdlib/stats-base-dists-chisquare-mgf

Chi-squared distribution moment-generating function (MGF).


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About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

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Moment-Generating Function

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Chi-squared distribution moment-generating function (MGF).

The moment-generating function for a chi-squared random variable is

Moment-generating function (MGF) for a chi-squared distribution.

where k is the degrees of freedom.

Installation

npm install @stdlib/stats-base-dists-chisquare-mgf

Usage

var mgf = require( '@stdlib/stats-base-dists-chisquare-mgf' );
mgf( t, k )

Evaluates the moment-generating function (MGF) for a chi-squared distribution with degrees of freedom k.

var y = mgf( 0.4, 2 );
// returns ~5.0

y = mgf( -1.0, 5.0 );
// returns ~0.0642

y = mgf( 0.0, 10.0 );
// returns 1.0

If provided NaN as any argument, the function returns NaN.

var y = mgf( NaN, 1.0 );
// returns NaN

y = mgf( 0.0, NaN );
// returns NaN

If provided t >= 0.5, the function returns NaN.

var y = mgf( 0.8, 1.0 );
// returns NaN

If provided k < 0, the function returns NaN.

var y = mgf( 2.0, -2.0 );
// returns NaN
mgf.factory( k )

Returns a function for evaluating the moment-generating function (MGF) for a chi-squared distribution with degrees of freedom k.

var mymgf = mgf.factory( 1.0 );

var y = mymgf( 0.2 );
// returns ~1.291

y = mymgf( 0.4 );
// returns ~2.236

Examples

var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-chisquare-mgf' );

var t;
var k;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu() * 0.5;
    k = randu() * 10.0;
    y = mgf( t, k );
    console.log( 'x: %d, k: %d, M_X(t;k): %d', t.toFixed( 4 ), k.toFixed( 4 ), y.toFixed( 4 ) );
}

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.

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License

See LICENSE.

Copyright © 2016-2024. The Stdlib Authors.

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Package last updated on 24 Feb 2024

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