@stdlib/stats-base-dists-chisquare-mgf
v0.2.3TypeScript
Chi-squared distribution moment-generating function (MGF).
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Published by The Stdlib Authors
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About stdlib...
Moment-Generating Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Chi-squared][chisquare-distribution] distribution moment-generating function (MGF).
The [moment-generating function][mgf] for a [chi-squared][chisquare-distribution] random variable is
where k is the degrees of freedom.
Installation
``bash`
npm install @stdlib/stats-base-dists-chisquare-mgf
Usage
`javascript`
var mgf = require( '@stdlib/stats-base-dists-chisquare-mgf' );
#### mgf( t, k )
Evaluates the [moment-generating function][mgf] (MGF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.
`javascript
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.
`javascript
var y = mgf( NaN, 1.0 );
// returns NaN
y = mgf( 0.0, NaN );
// returns NaN
`
If provided t >= 0.5, the function returns NaN.
`javascript`
var y = mgf( 0.8, 1.0 );
// returns NaN
If provided k < 0, the function returns NaN.
`javascript`
var y = mgf( 2.0, -2.0 );
// returns NaN
#### mgf.factory( k )
Returns a function for evaluating the [moment-generating function][mgf] (MGF) for a [chi-squared][chisquare-distribution] distribution with degrees of freedom k.
`javascript
var mymgf = mgf.factory( 1.0 );
var y = mymgf( 0.2 );
// returns ~1.291
y = mymgf( 0.4 );
// returns ~2.236
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var mgf = require( '@stdlib/stats-base-dists-chisquare-mgf' );
var opts = {
'dtype': 'float64'
};
var t = uniform( 10, 0.0, 0.5, opts );
var k = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, k: %0.4f, M_X(t;k): %0.4f', t, k, mgf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/chisquare/mgf.h"
#### stdlib_base_dists_chisquare_mgf( t, k )
Evaluates the moment-generating function (MGF) for a chi-squared distribution with degrees of freedom k at a value t.
`c`
double out = stdlib_base_dists_chisquare_mgf( 0.4, 2.0 );
// returns ~5.0
The function accepts the following arguments:
- t: [in] double input value.[in] double
- k: degrees of freedom (must be nonnegative).
`c`
double stdlib_base_dists_chisquare_mgf( const double t, const double k );
$3
`c
#include "stdlib/stats/base/dists/chisquare/mgf.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v * ( max - min ) );
}
int main( void ) {
double result;
double t;
double k;
int i;
for ( i = 0; i < 10; i++ ) {
t = random_uniform( -0.5, 0.4 );
k = random_uniform( 0.1, 10.0 );
result = stdlib_base_dists_chisquare_mgf( t, k );
printf( "t: %lf, k: %lf, M_X(t;k): %lf \n", t, k, result );
}
}
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-chisquare-mgf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-chisquare-mgf/main/LICENSE
[chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution
[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function