Logarithm of Probability Density Function

Logistic distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a logistic random variable is

where mu is the location parameter and s is the scale parameter.

Installation

npm install @stdlib/stats-base-dists-logistic-logpdf

Usage

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

logpdf( x, mu, s )

Evaluates the logarithm of the probability density function (PDF) for a logistic distribution with parameters mu (location parameter) and s (scale parameter).

var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.254

y = logpdf( -1.0, 4.0, 4.0 );
// returns ~-3.14

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

var y = logpdf( NaN, 0.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

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

If provided s < 0, the function returns NaN.

var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaN

If provided s = 0, the function evaluates the logarithm of the PDF of a degenerate distribution centered at mu.

var y = logpdf( 2.0, 8.0, 0.0 );
// returns -Infinity

y = logpdf( 8.0, 8.0, 0.0 );
// returns Infinity

logpdf.factory( mu, s )

Returns a function for evaluating the logarithm of the probability density function (PDF) of a logistic distribution with parameters mu (location parameter) and s (scale parameter).

var mylogpdf = logpdf.factory( 10.0, 2.0 );

var y = mylogpdf( 10.0 );
// returns ~-2.079

y = mylogpdf( 5.0 );
// returns ~-3.351

Notes

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

Examples

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

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, 0.0, 10.0, opts );
var mu = uniform( 10, 0.0, 10.0, opts );
var s = uniform( 10, 0.0, 10.0, opts );

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

C APIs

Usage

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

stdlib_base_dists_logistic_logpdf( x, mu, s )

Evaluates the logarithm of the probability density function (PDF) for a logistic distribution with location parameter mu and scale parameter s at a value x.

double out = stdlib_base_dists_logistic_logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.254

The function accepts the following arguments:

• x: [in] double input value.
• mu: [in] double location parameter.
• s: [in] double scale parameter.

double stdlib_base_dists_logistic_logpdf( const double x, const double mu, const double s );

Examples

#include "stdlib/stats/base/dists/logistic/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 s;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( -5.0, 5.0 );
        mu = random_uniform( -5.0, 5.0 );
        s = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_logistic_logpdf( x, mu, s );
        printf( "x: %lf, µ: %lf, s: %lf, ln(f(x;µ,s)): %lf\n", x, mu, s, 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.