Moment-Generating Function

Planck (discrete exponential) distribution moment-generating function (MGF).

The moment-generating function for a Planck random variable is

where λ is the shape parameter.

Installation

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

Usage

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

mgf( t, lambda )

Evaluates the moment-generating function (MGF) of a Planck (discrete exponential) distribution with shape parameter lambda.

var y = mgf( 0.2, 0.5 );
// returns ~1.5181

y = mgf( 0.4, 1.5 );
// returns ~1.1645

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 a shape parameter lambda which is nonpositive, the function returns NaN.

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

mgf.factory( lambda )

Returns a function for evaluating the moment-generating function of a Planck (discrete exponential) distribution with shape parameter lambda.

var mymgf = mgf.factory( 0.8 );
var y = mymgf( -0.2 );
// returns ~0.8711

Examples

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

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, 0.1, 5.0, opts );
var t = uniform( 10, 0.0, 10.0, opts );

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

C APIs

Usage

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

stdlib_base_dists_planck_mgf( t, lambda )

Evaluates the moment-generating function (MGF) for a Planck distribution with shape parameter lambda at a value t.

double out = stdlib_base_dists_planck_mgf( 0.2, 0.5 );
// returns ~1.5181

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/planck/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 < 10; i++ ) {
        t = random_uniform( 0.0, 10.0 );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_planck_mgf( t, lambda );
        printf( "t: %lf, λ: %lf, M_X(t;λ): %lf\n", t, lambda, y );
    }
    return 0;
}

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.