Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function (PDF) for an exponential distribution.

The probability density function (PDF) for an exponential random variable is

where λ is the rate parameter.

Installation

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

Usage

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

logpdf( x, lambda )

Evaluates the natural logarithm of the probability density function (PDF) for an exponential distribution with rate parameter lambda.

var y = logpdf( 2.0, 0.3 );
// returns ~-1.804

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

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

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

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

If provided lambda < 0, the function returns NaN.

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

logpdf.factory( lambda )

Returns a function for evaluating the natural logarithm of the probability density function (PDF) for an exponential distribution with rate parameter lambda.

var mylogpdf = logpdf.factory( 0.1 );

var y = mylogpdf( 8.0 );
// returns ~-3.103

y = mylogpdf( 5.0 );
// returns ~-2.803

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-exponential-logpdf' );

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

logEachMap( 'x: %0.4f, λ: %0.4f, ln(f(x;λ)): %0.4f', x, lambda, logpdf );

C APIs

Usage

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

stdlib_base_dists_exponential_logpdf( x, lambda )

Evaluates the natural logarithm of the probability density function (PDF) for an exponential distribution with rate parameter lambda.

double out = stdlib_base_dists_exponential_logpdf( 2.0, 0.7 );
// returns ~0.173

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/exponential/logpdf.h"
#include "stdlib/constants/float64/eps.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, 100.0 );
        lambda = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 100.0 );
        y = stdlib_base_dists_exponential_logpdf( x, lambda );
        printf( "x: %lf, λ: %lf, ln(f(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.