Probability Mass Function

Planck (discrete exponential) distribution probability mass function (PMF).

The probability mass function (PMF) for a Planck random variable is defined as

where λ is the shape parameter. The random variable X denotes the count of events in a quantized system.

Installation

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

Usage

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

pmf( x, lambda )

Evaluates the probability mass function (PMF) of a Planck (discrete exponential) distribution with shape parameter lambda.

var y = pmf( 4.0, 0.3 );
// returns ~0.0781

y = pmf( 2.0, 1.7 );
// returns ~0.0273

y = pmf( -1.0, 2.5 );
// returns 0.0

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

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

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

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

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

pmf.factory( lambda )

Returns a function for evaluating the probability mass function (PMF) of a Planck (discrete exponential) distribution with shape parameter lambda.

var mypmf = pmf.factory( 0.5 );
var y = mypmf( 3.0 );
// returns ~0.0878

y = mypmf( 1.0 );
// returns ~0.2387

Examples

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 5, opts );
var lambda = uniform( 10, 0.1, 5.0, opts );

logEachMap( 'x: %d, λ: %0.4f, P(X = x; λ): %0.4f', x, lambda, pmf );

C APIs

Usage

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

stdlib_base_dists_planck_pmf( x, lambda )

Evaluates the probability mass function for a Planck (discrete exponential) distribution with input value x and shape parameter lambda.

double out = stdlib_base_dists_planck_pmf( 4.0, 0.3 );
// returns ~0.0781

The function accepts the following arguments:

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

double stdlib_base_dists_planck_pmf( const double x, const double lambda );

Examples

#include "stdlib/stats/base/dists/planck/pmf.h"
#include "stdlib/math/base/special/round.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 x;
    double lambda;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = stdlib_base_round( random_uniform( 0.0, 11.0 ) );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_planck_pmf( x, lambda );
        printf( "x: %.0f, λ: %lf, P(X = x; λ): %lf\n", x, 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.