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 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/uniform/mgf.h"

stdlib_base_dists_uniform_mgf( t, a, b )

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

double out = stdlib_base_dists_uniform_mgf( 2.0, 0.0, 4.0 );
// returns ~372.495

The function accepts the following arguments:

• x: [in] double input value.
• a: [in] double minimum support.
• b: [in] double maximum support.

double stdlib_base_dists_uniform_mgf( const double t, const double a, const double b );

Examples

#include "stdlib/stats/base/dists/uniform/mgf.h"
#include <stdlib.h>
#include <stdio.h>

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 a;
    double b;
    double t;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        t = random_uniform( -10.0, 10.0 );
        a = random_uniform( -20.0, 0.0 );
        b = random_uniform( a, a+40.0 );
        y = stdlib_base_dists_uniform_mgf( t, a, b );
        printf( "t: %lf, a: %lf, b: %lf, M_X(t;a,b): %lf\n", t, a, b, y );
    }
}

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.