Logarithm of Probability Mass Function

Evaluate the logarithm of the probability mass function (PMF) for a Planck (discrete exponential) distribution.

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

where λ is the shape parameter and x denotes the count of events in a quantized system.

Installation

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

Usage

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

logpmf( x, lambda )

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

var y = logpmf( 4.0, 0.3 );
// returns ~-2.5502

y = logpmf( 2.0, 1.7 );
// returns ~-3.6017

y = logpmf( -1.0, 2.5 );
// returns -Infinity

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

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

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

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

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

logpmf.factory( lambda )

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

var mylogpmf = logpmf.factory( 0.5 );
var y = mylogpmf( 3.0 );
// returns ~-2.4328

y = mylogpmf( 1.0 );
// returns ~-1.4328

Notes

• In virtually all cases, using the logpmf or logcdf functions is preferable to manually computing the logarithm of the pmf or cdf, respectively, since the latter is prone to overflow and underflow.

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

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, ln( P( X = x; λ ) ): %0.4f', x, lambda, logpmf );

C APIs

Usage

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

stdlib_base_dists_planck_logpmf( x, lambda )

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

double out = stdlib_base_dists_planck_logpmf( 4.0, 0.3 );
// returns ~-2.5502

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/planck/logpmf.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_logpmf( x, lambda );
        printf( "x: %.0f, λ: %lf, ln(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.