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Cumulative Distribution Function

Planck (discrete exponential) distribution cumulative distribution function.

The cumulative distribution function for a Planck random variable is

$$F(x;\lambda) = 1 - e^{-\lambda (\lfloor x \rfloor + 1)}$$

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-cdf

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

cdf( x, lambda )

Evaluates the cumulative distribution function for a Planck (discrete exponential) distribution with shape parameter lambda.

var y = cdf( 2.0, 0.5 );
// returns ~0.7769

y = cdf( 2.0, 1.5 );
// returns ~0.9889

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

var y = cdf( NaN, 0.5 );
// returns NaN

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

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

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

cdf.factory( lambda )

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

var mycdf = cdf.factory( 1.5 );
var y = mycdf( 3.0 );
// returns ~0.9975

y = mycdf( 1.0 );
// returns ~0.9502

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var cdf = require( '@stdlib/stats-base-dists-planck-cdf' );

var x = discreteUniform( 10, 0, 5 );
var lambda = uniform( 10, 0.1, 5.0 );

var y;
var i;
for ( i = 0; i < lambda.length; i++ ) {
    y = cdf( x[ i ], lambda[ i ] );
    console.log( 'x: %d, λ: %d, F(x;λ): %d', x[ i ].toFixed( 4 ), lambda[ i ].toFixed( 4 ), y.toFixed( 4 ) );
}

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C APIs

Usage

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

stdlib_base_dists_planck_cdf( x, lambda )

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

double out = stdlib_base_dists_planck_cdf( 2.0, 0.5 );
// returns ~0.7769

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/planck/cdf.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 x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 11.0 );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_planck_cdf( x, lambda );
        printf( "x: %lf, λ: %lf, F(x;λ): %lf\n", x, lambda, y );
    }
}

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.