Probability Density Function

Degenerate distribution probability density function (PDF).

Strictly speaking, as a discrete distribution, a degenerate has no probability density function (PDF). Extending the notion of a PDF, we conceptualize the PDF of a degenerate as an infinitely tall spike centered at mu. More formally,

where delta is the Dirac delta function.

Installation

npm install @stdlib/stats-base-dists-degenerate-pdf

Usage

var pdf = require( '@stdlib/stats-base-dists-degenerate-pdf' );

pdf( x, mu )

Evaluates the PDF of a degenerate distribution centered at mu.

var y = pdf( 2.0, 8.0 );
// returns 0.0

y = pdf( 8.0, 8.0 );
// returns Infinity

pdf.factory( mu )

Returns a function for evaluating the PDF of a degenerate distribution centered at mu.

var mypdf = pdf.factory( 10.0 );

var y = mypdf( 10.0 );
// returns Infinity

y = mypdf( 5.0 );
// returns 0.0

y = mypdf( 12.0 );
// returns 0.0

Examples

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

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 100, 0, 5, opts );
var mu = discreteUniform( 100, 0, 5, opts );

logEachMap( 'x: %d, µ: %d, f(x;µ): %0.4f', x, mu, pdf );

C APIs

Usage

#include "stdlib/stats/base/dists/degenerate/pdf.h"

stdlib_base_dists_degenerate_pdf( x, mu )

Evaluates the PDF of a degenerate distribution centered at mu.

double out = stdlib_base_dists_degenerate_pdf( 2.0, 3.0 );
// returns 0.0

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double constant value of the distribution.

double stdlib_base_dists_degenerate_pdf( const double x, const double mu );

Examples

#include "stdlib/stats/base/dists/degenerate/pdf.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 result;
    double mu;
    double x;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
        mu = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
        result = stdlib_base_dists_degenerate_pdf( x, mu );
        printf( "x: %lf, µ: %lf, f(x;µ): %lf \n", x, mu, result );
    }
}

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.