Cumulative Distribution Function

Pareto (Type I) distribution cumulative distribution function.

The cumulative distribution function for a Pareto (Type I) random variable is

and zero otherwise. In the equation, alpha > 0 is the shape parameter and beta > 0 is the scale parameter.

Installation

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

Usage

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

cdf( x, alpha, beta )

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

var y = cdf( 2.0, 1.0, 1.0 );
// returns 0.5

y = cdf( 5.0, 2.0, 4.0 );
// returns ~0.36

y = cdf( 4.0, 2.0, 2.0 );
// returns 0.75

y = cdf( 1.9, 2.0, 2.0 );
// returns 0.0

y = cdf( +Infinity, 4.0, 2.0 );
// returns 1.0

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

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

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

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

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

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

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

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

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

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

cdf.factory( alpha, beta )

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

var mycdf = cdf.factory( 10.0, 2.0 );
var y = mycdf( 3.0 );
// returns ~0.983

y = mycdf( 2.5 );
// returns ~0.893

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    x = randu() * 8.0;
    alpha = randu() * 5.0;
    beta = randu() * 5.0;
    y = cdf( 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.