@stdlib/stats-base-dists-normal-mgf
v0.3.1TypeScript
Normal 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]
> [Normal][normal-distribution] distribution moment-generating function (MGF).
The [moment-generating function][mgf] for a [normal][normal-distribution] random variable is
where mu is the mean and sigma > 0 is the standard deviation.
Installation
``bash`
npm install @stdlib/stats-base-dists-normal-mgf
Usage
`javascript`
var mgf = require( '@stdlib/stats-base-dists-normal-mgf' );
#### mgf( t, mu, sigma )
Evaluates the [moment-generating function][mgf] (MGF) for a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`javascript
var y = mgf( 2.0, 0.0, 1.0 );
// returns ~7.389
y = mgf( 0.0, 0.0, 1.0 );
// returns 1.0
y = mgf( -1.0, 4.0, 2.0 );
// returns ~0.1353
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = mgf( NaN, 0.0, 1.0 );
// returns NaN
y = mgf( 0.0, NaN, 1.0 );
// returns NaN
y = mgf( 0.0, 0.0, NaN );
// returns NaN
`
If provided sigma <= 0, the function returns NaN.
`javascript
var y = mgf( 2.0, 0.0, 0.0 );
// returns NaN
y = mgf( 2.0, 0.0, -1.0 );
// returns NaN
`
#### mgf.factory( mu, sigma )
Returns a function for evaluating the [moment-generating function][mgf] (MGF) of a [normal][normal-distribution] distribution with parameters mu and sigma.
`javascript
var mymgf = mgf.factory( 4.0, 2.0 );
var y = mymgf( 1.0 );
// returns ~403.429
y = mymgf( 0.5 );
// returns ~12.182
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var mgf = require( '@stdlib/stats-base-dists-normal-mgf' );
var opts = {
'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
var t = uniform( 10, 0.0, 10.0, opts );
logEachMap( 't: %0.4f, µ: %0.4f, σ: %0.4f, M_X(t;µ,σ): %0.4f', t, mu, sigma, mgf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/normal/mgf.h"
#### stdlib_base_dists_normal_mgf( t, mu, sigma )
Evaluates the [moment-generating function][mgf] (MGF) for a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`c`
double y = stdlib_base_dists_normal_mgf( 2.0, 0.0, 1.0 );
// returns ~7.389
The function accepts the following arguments:
- t: [in] double input value.[in] double
- mu: mean.[in] double
- sigma: standard deviation.
`c`
double stdlib_base_dists_normal_mgf( const double t, const double mu, const double sigma );
$3
`c
#include "stdlib/stats/base/dists/normal/mgf.h"
#include "stdlib/constants/float64/eps.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 sigma;
double mu;
double t;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
t = random_uniform( 0.0, 1.0 );
mu = random_uniform( -50.0, 50.0 );
sigma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
y = stdlib_base_dists_normal_mgf( t, mu, sigma );
printf( "t: %lf, µ: %lf, σ: %lf, M_X(t;µ,σ): %lf\n", t, mu, sigma, y );
}
}
`
*
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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[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
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[deno-readme]: https://github.com/stdlib-js/stats-base-dists-normal-mgf/blob/deno/README.md
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[esm-url]: https://github.com/stdlib-js/stats-base-dists-normal-mgf/tree/esm
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-normal-mgf/main/LICENSE
[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function