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.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Moment-Generating Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Poisson][poisson-distribution] distribution moment-generating function (MGF).

The [moment-generating function][mgf] for a [Poisson][poisson-distribution] random variable is

Moment-generating function (MGF) for a Poisson distribution.

where lambda > 0 is the mean parameter.

Installation

``bash npm install @stdlib/stats-base-dists-poisson-mgf`

`Usage`

`javascript var mgf = require( '@stdlib/stats-base-dists-poisson-mgf' );`

#### mgf( t, lambda )

Evaluates the moment-generating function ([MGF][mgf]) for a [Poisson][poisson-distribution] distribution with parameter lambda (mean).

`javascript var y = mgf( 1.0, 1.5 ); // returns ~13.163

y = mgf( 0.5, 0.5 ); // returns ~1.383`

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

`javascript var y = mgf( NaN, 0.5 ); // returns NaN

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

If provided lambda <= 0, the function returns NaN.

`javascript var y = mgf( -2.0, -1.0 ); // returns NaN

y = mgf( 0.1, 0.0 ); // returns NaN`

#### mgf.factory( lambda )

Returns a function for evaluating the [moment-generating function][mgf] of a [Poisson][poisson-distribution] distribution with parameter lambda (mean).

`javascript var mymgf = mgf.factory( 2.0 ); var y = mymgf( 0.1 ); // returns ~1.234`

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var mgf = require( '@stdlib/stats-base-dists-poisson-mgf' );

var opts = { 'dtype': 'float64' }; var t = uniform( 10, 0.0, 5.0, opts ); var lambda = uniform( 10, 0.0, 5.0, opts );

logEachMap( 't: %0.4f, λ: %0.4f, M_X(t;λ): %0.4f', t, lambda, mgf );`

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/poisson/mgf.h"`

#### stdlib_base_dists_poisson_mgf( t, lambda )

Evaluates the moment-generating function ([MGF][mgf]) for a [Poisson][poisson-distribution] distribution with parameter lambda (mean).

`c double out = stdlib_base_dists_poisson_mgf( 1.0, 1.5 ); // returns ~13.163`

The function accepts the following arguments:

- t: [in] doubleinput value. - lambda:[in] double mean parameter.

`c double stdlib_base_dists_poisson_mgf( const double t, const double lambda );`

`$3`

`c #include "stdlib/stats/base/dists/poisson/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 lambda; double t; double y; int i;

for ( i = 0; i < 25; i++ ) { t = random_uniform( -2.0, 2.0 ); lambda = random_uniform( 0.1, 10.0 ); y = stdlib_base_dists_poisson_mgf( t, lambda ); printf( "t: %lf, λ: %lf, M_X(t;λ): %lf\n", t, lambda, 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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-poisson-mgf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-poisson-mgf

[test-image]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/actions/workflows/test.yml?query=branch:v0.3.1

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-poisson-mgf/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-poisson-mgf?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[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-poisson-mgf/tree/deno [deno-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/tree/umd [umd-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/tree/esm [esm-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/stats-base-dists-poisson-mgf/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson-mgf/main/LICENSE

[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function


  
    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.

  When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`Moment-Generating Function`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> [Poisson][poisson-distribution] distribution moment-generating function (MGF).

The [moment-generating function][mgf] for a [Poisson][poisson-distribution] random variable is

where lambda > 0 is the mean parameter.

`Installation`

``bash npm install @stdlib/stats-base-dists-poisson-mgf `

`Usage`

`javascript var mgf = require( '@stdlib/stats-base-dists-poisson-mgf' ); `

#### mgf( t, lambda )

Evaluates the moment-generating function ([MGF][mgf]) for a [Poisson][poisson-distribution] distribution with parameter lambda (mean).

`javascript var y = mgf( 1.0, 1.5 ); // returns ~13.163

y = mgf( 0.5, 0.5 ); // returns ~1.383 `

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

`javascript var y = mgf( NaN, 0.5 ); // returns NaN

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

If provided lambda <= 0, the function returns NaN.

`javascript var y = mgf( -2.0, -1.0 ); // returns NaN

y = mgf( 0.1, 0.0 ); // returns NaN `

#### mgf.factory( lambda )

Returns a function for evaluating the [moment-generating function][mgf] of a [Poisson][poisson-distribution] distribution with parameter lambda (mean).

`javascript var mymgf = mgf.factory( 2.0 ); var y = mymgf( 0.1 ); // returns ~1.234 `

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var mgf = require( '@stdlib/stats-base-dists-poisson-mgf' );

var opts = { 'dtype': 'float64' }; var t = uniform( 10, 0.0, 5.0, opts ); var lambda = uniform( 10, 0.0, 5.0, opts );

logEachMap( 't: %0.4f, λ: %0.4f, M_X(t;λ): %0.4f', t, lambda, mgf ); `

*

`C APIs`

`$3`

`c #include "stdlib/stats/base/dists/poisson/mgf.h" `

#### stdlib_base_dists_poisson_mgf( t, lambda )

Evaluates the moment-generating function ([MGF][mgf]) for a [Poisson][poisson-distribution] distribution with parameter lambda (mean).

`c double out = stdlib_base_dists_poisson_mgf( 1.0, 1.5 ); // returns ~13.163 `

The function accepts the following arguments:

- t: [in] double input value. - lambda: [in] double mean parameter.

`c double stdlib_base_dists_poisson_mgf( const double t, const double lambda ); `

`$3`

`c #include "stdlib/stats/base/dists/poisson/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 lambda; double t; double y; int i;

for ( i = 0; i < 25; i++ ) { t = random_uniform( -2.0, 2.0 ); lambda = random_uniform( 0.1, 10.0 ); y = stdlib_base_dists_poisson_mgf( t, lambda ); printf( "t: %lf, λ: %lf, M_X(t;λ): %lf\n", t, lambda, y ); } } `

*

`Notice`

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`

[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-poisson-mgf.svg [npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-poisson-mgf

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson-mgf/main/LICENSE

[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function