Exponential

Exponential distribution.

Installation

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

Usage

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

exponential

Exponential distribution.

var dist = exponential;
// returns {...}

The namespace contains the following distribution functions:

• cdf( x, lambda ): exponential distribution cumulative distribution function.
• logcdf( x, lambda ): evaluate the natural logarithm of the cumulative distribution function for an exponential distribution.
• logpdf( x, lambda ): evaluate the natural logarithm of the probability density function (PDF) for an exponential distribution.
• mgf( t, lambda ): exponential distribution moment-generating function (MGF).
• pdf( x, lambda ): exponential distribution probability density function (PDF).
• quantile( p, lambda ): exponential distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• entropy( lambda ): exponential distribution differential entropy.
• kurtosis( lambda ): exponential distribution excess kurtosis.
• mean( lambda ): exponential distribution expected value.
• median( lambda ): exponential distribution median.
• mode( lambda ): exponential distribution mode.
• skewness( lambda ): exponential distribution skewness.
• stdev( lambda ): exponential distribution standard deviation.
• variance( lambda ): exponential distribution variance.

The namespace contains a constructor function for creating an exponential distribution object.

• Exponential( [lambda] ): exponential distribution constructor.

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

var dist = new Exponential( 2.0 );

var y = dist.logpdf( 0.8 );
// returns ~-0.907

Examples

var Float64Array = require( '@stdlib/array-float64' );
var randomExponential = require( '@stdlib/random-array-exponential' );
var dcusum = require( '@stdlib/blas-ext-base-dcusum' );
var exponential = require( '@stdlib/stats-base-dists-exponential' );

// Simulate interarrival times of customers entering a store:
var lambda = 0.5; // Average rate (customers per minute)
var numCustomers = 10;

// Generate interarrival times using the exponential distribution:
var interarrivalTimes = randomExponential( numCustomers, lambda, {
    'dtype': 'float64'
});

console.log( 'Simulated interarrival times for ' + numCustomers + ' customers: ' );
console.log( interarrivalTimes );

// Calculate cumulative arrival times by computing the cumulative sum of interarrival times:
var arrivalTimes = new Float64Array( interarrivalTimes.length );
dcusum( interarrivalTimes.length, 0.0, interarrivalTimes, 1, arrivalTimes, 1 );

console.log( '\nCustomer arrival times: ' );
console.log( arrivalTimes );

// Probability that a customer arrives within two minutes:
var x = 2.0;
var prob = exponential.cdf( x, lambda );
console.log( '\nProbability that a customer arrives within ' + x + ' minutes: ' + prob.toFixed(4) );

// Expected time until the next customer arrives:
var mean = exponential.mean( lambda );
console.log( 'Expected interarrival time: ' + mean + ' minutes' );

var dist = new exponential.Exponential( lambda );

var median = dist.median;
console.log( 'Median interarrival time: ' + median + ' minutes' );

// Evaluate the PDF at x = 1.0:
var out = dist.pdf( 1.0 );
console.log( 'PDF at x = 1: ' + out.toFixed(4) );

// Evaluate the MGF at t = 0.1:
out = dist.mgf( 0.1 );
console.log( 'MGF at t = 0.1: ' + out.toFixed(4) );

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.