Probability Density Function

Pareto (Type I) distribution probability density function (PDF).

The probability density function (PDF) for a Pareto (Type I) random variable is

where alpha > 0 is the shape parameter and beta > 0 is the scale parameter.

Installation

npm install @stdlib/stats-base-dists-pareto-type1-pdf

Usage

var pdf = require( '@stdlib/stats-base-dists-pareto-type1-pdf' );

pdf( x, alpha, beta )

Evaluates the probability density function (PDF) for a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var y = pdf( 4.0, 1.0, 1.0 );
// returns ~0.063

y = pdf( 20.0, 1.0, 10.0 );
// returns 0.025

y = pdf( 7.0, 2.0, 6.0 );
// returns ~0.21

y = pdf( 7.0, 6.0, 3.0 );
// returns ~0.005

y = pdf( 1.0, 4.0, 2.0 );
// returns 0.0

y = pdf( 1.5, 4.0, 2.0 );
// returns 0.0

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

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

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

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

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

var y = pdf( 2.0, -1.0, 0.5 );
// returns NaN

y = pdf( 2.0, 0.0, 0.5 );
// returns NaN

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

var y = pdf( 2.0, 0.5, -1.0 );
// returns NaN

y = pdf( 2.0, 0.5, 0.0 );
// returns NaN

pdf.factory( alpha, beta )

Returns a function for evaluating the probability density function (PDF) (CDF) of a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var mypdf = pdf.factory( 0.5, 0.5 );
var y = mypdf( 0.8 );
// returns ~0.494

y = mypdf( 2.0 );
// returns ~0.125

Examples

var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-pareto-type1-pdf' );

var alpha;
var beta;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 8.0;
    alpha = randu() * 4.0;
    beta = randu() * 4.0;
    y = pdf( x, alpha, beta );
    console.log( 'x: %d, α: %d, β: %d, f(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.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 © 2016-2024. The Stdlib Authors.