README.md

About stdlib...

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Probability Density Function

Laplace distribution probability density function (PDF).

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

$$f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)$$

where mu is the location parameter and b > 0 is the scale parameter (also called diversity).

Usage

import pdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-laplace-pdf@deno/mod.js';

You can also import the following named exports from the package:

import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-laplace-pdf@deno/mod.js';

pdf( x, mu, b )

Evaluates the probability density function (PDF) for a Laplace distribution with parameters mu (location parameter) and b > 0 (scale parameter).

var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.068

y = pdf( -1.0, 2.0, 3.0 );
// returns ~0.061

y = pdf( 2.5, 2.0, 3.0 );
// returns ~0.141

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

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

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

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

If provided b <= 0, the function returns NaN.

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

y = pdf( 2.0, 8.0, 0.0 );
// returns NaN

pdf.factory( mu, b )

Returns a function for evaluating the PDF of a Laplace distribution with parameters mu (location parameter) and b > 0 (scale parameter).

var mypdf = pdf.factory( 10.0, 2.0 );

var y = mypdf( 10.0 );
// returns 0.25

y = mypdf( 5.0 );
// returns ~0.021

y = mypdf( 12.0 );
// returns ~0.092

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import pdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-laplace-pdf@deno/mod.js';

var mu;
var b;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    b = randu() * 10.0;
    y = pdf( x, mu, b );
    console.log( 'x: %d, µ: %d, b: %d, f(x;µ,b): %d', x.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}

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Notice

This package is part of stdlib, a standard library 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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.