# @stdlib/stats-base-dists-discrete-uniform-mgf

0.1.1 • Public • Published

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# Moment-Generating Function

Discrete uniform distribution moment-generating function (MGF).

The moment-generating function for a discrete uniform random variable is

where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a <= b`.

## Installation

`npm install @stdlib/stats-base-dists-discrete-uniform-mgf`

## Usage

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

#### mgf( t, a, b )

Evaluates the moment-generating function (MGF) for a discrete uniform distribution with parameters `a` (minimum support) and `b` (maximum support).

```var y = mgf( 2.0, 0, 4 );
// returns ~689.475

y = mgf( -0.2, 0, 4 );
// returns ~0.697

y = mgf( 2.0, 0, 1 );
// returns ~4.195```

If `a` or `b` is not an integer value, the function returns `NaN`.

```var y = mgf( 0.2, 1, 5.5 );
// returns NaN```

If provided `a > b`, the function returns `NaN`.

```var y = mgf( 0.5, 3, 2);
// returns NaN```

If provided `NaN` for any parameter, the function returns `NaN`.

```var y = mgf( NaN, 0, 1 );
// returns NaN

y = mgf( 0.0, NaN, 1 );
// returns NaN

y = mgf( 0.0, 0, NaN );
// returns NaN```

#### mgf.factory( a, b )

Returns a function for evaluating the moment-generating function (MGF) of a discrete uniform distribution with parameters `a` (minimum support) and `b` (maximum support).

```var mymgf = mgf.factory( 6, 7 );
var y = mymgf( 0.1 );
// returns ~1.918

y = mymgf( 1.1 );
// returns ~1471.722```

## Examples

```var randint = require( '@stdlib/random-base-discrete-uniform' );
var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-discrete-uniform-mgf' );

var randa = randint.factory( 0, 5 );
var randb = randint.factory();
var a;
var b;
var t;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
t = randu();
a = randa();
b = randb( a, a+randa() );
v = mgf( t, a, b );
console.log( 't: %d, a: %d, b: %d, M_X(t;a,b): %d', t.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.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.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-discrete-uniform-mgf`

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