Moment-Generating Function

Exponential distribution moment-generating function (MGF).

The moment-generating function for an exponential random variable is

where lambda > 0 is the rate parameter. For t >= lambda, the MGF is undefined.

Installation

npm install @stdlib/stats-base-dists-exponential-mgf

Usage

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

mgf( t, lambda )

Evaluates the moment-generating function (MGF) for an exponential distribution.

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

y = mgf( 0.4, 1.2 );
// returns 1.5

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

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

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

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

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

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

mgf.factory( lambda )

Returns a function for evaluating the moment-generating function of an exponential distribution with parameter lambda(rate parameter).

var mymgf = mgf.factory( 4.0 );
var y = mymgf( 3.0 );
// returns 4.0

Examples

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

var opts = {
    'dtype': 'float64'
};
var t = uniform( 10, 0.0, 10.0, opts );
var lambda = uniform( 10, 0.0, 10.0, opts );

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

C APIs

Usage

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

stdlib_base_dists_exponential_mgf( t, lambda )

Evaluates the moment-generating function (MGF) for an exponential distribution.

double out = stdlib_base_dists_exponential_mgf( 2.0, 3.0 );
// returns 3.0

The function accepts the following arguments:

• t: [in] double input value.
• lambda: [in] double rate parameter.

double stdlib_base_dists_exponential_mgf( const double t, const double lambda );

Examples

#include "stdlib/stats/base/dists/exponential/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 lambda;
    double t;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        t = random_uniform( -1.0, 1.0 );
        lambda = random_uniform( 1.1, 10.0 );
        y = stdlib_base_dists_exponential_mgf( t, lambda );
        printf( "t: %lf, λ: %lf, M_X(t;λ): %lf\n", t, lambda, 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.