Logarithm of Probability Density Function

Degenerate distribution logarithm of probability density function (logPDF).

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 distribution 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-logpdf

Usage

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

logpdf( x, mu )

Evaluates the natural logarithm of the PDF of a degenerate distribution centered at mu.

var y = logpdf( 2.0, 8.0 );
// returns -Infinity

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

logpdf.factory( mu )

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

var mylogpdf = logpdf.factory( 10.0 );

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

y = mylogpdf( 5.0 );
// returns -Infinity

y = mylogpdf( 12.0 );
// returns -Infinity

Examples

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

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

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

C APIs

Usage

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

stdlib_base_dists_degenerate_logpdf( x, mu )

Evaluates the natural logarithm of the probability density function (logPDF) for a degenerate distribution.

double out = stdlib_base_dists_degenerate_logpdf( 2.0, 3.0 );
// returns -Infinity

The function accepts the following arguments:

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

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

Examples

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

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 5.0 );
        mu = random_uniform( 0.0, 5.0 );
        y = stdlib_base_dists_degenerate_logpdf( x, mu );
        printf( "x: %lf, µ: %lf, ln(f(x;µ)): %lf\n", x, mu, 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.