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

0.2.1 • Public • Published

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# Moment-Generating Function

Uniform distribution moment-generating function (MGF).

The moment-generating function for a continuous 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-uniform-mgf`

## Usage

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

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

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

```var y = mgf( 2.0, 0.0, 4.0 );
// returns ~372.495

y = mgf( -0.2, 0.0, 4.0 );
// returns ~0.688

y = mgf( 2.0, 0.0, 1.0 );
// returns ~3.195```

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

```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 `a >= b`, the function returns `NaN`.

```var y = mgf( 0.5, 3.0, 2.0 );
// returns NaN

y = mgf( 0.5, 3.0, 3.0 );
// returns NaN```

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

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

```var mymgf = mgf.factory( 6.0, 7.0 );
var y = mymgf( 0.1 );
// returns ~1.916

y = mymgf( 1.1 );
// returns ~1339.321```

## Examples

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

var a;
var b;
var t;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
t = randu();
a = randu() * 5.0;
b = a + (randu() * 5.0);
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-uniform-mgf`

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