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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.
npm install @stdlib/stats-base-dists-chisquare-mgf
var mgf = require( '@stdlib/stats-base-dists-chisquare-mgf' );
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
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
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 ) );
}
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.
See LICENSE.
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