Probability Density Function

Exponential distribution probability density function (PDF).

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-pdf

Usage

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

pdf( x, lambda )

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

var y = pdf( 2.0, 0.3 );
// returns ~0.165

y = pdf( 2.0, 1.0 );
// returns ~0.135

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

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

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

If provided lambda < 0, the function returns NaN.

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

pdf.factory( lambda )

Partially applies lambda to create a reusable function for evaluating the PDF.

var mypdf = pdf.factory( 0.1 );

var y = mypdf( 8.0 );
// returns ~0.045

y = mypdf( 5.0 );
// returns ~0.06

Examples

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

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, f(x;λ): %0.4f', x, lambda, pdf );

C APIs

Usage

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

stdlib_base_dists_exponential_pdf( x, lambda )

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

double out = stdlib_base_dists_exponential_pdf( 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_pdf( const double x, const double lambda );

Examples

#include "stdlib/stats/base/dists/exponential/pdf.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( 0.0, 100.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
        y = stdlib_base_dists_exponential_pdf( x, lambda );
        printf( "x: %lf, λ: %lf, 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.