@stdlib/stats-base-dists-chisquare-mgf
v0.2.2
Published
Chi-squared distribution moment-generating function (MGF).
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Moment-Generating Function
Chi-squared distribution moment-generating function (MGF).
The moment-generating function for a chi-squared random variable is
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.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.