Cumulative Distribution Function
Pareto (Type I) distribution cumulative distribution function.
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 );
y = cdf( 5.0, 2.0, 4.0 );
y = cdf( 4.0, 2.0, 2.0 );
y = cdf( 1.9, 2.0, 2.0 );
y = cdf( +Infinity, 4.0, 2.0 );
If provided NaN
as any argument, the function returns NaN
.
var y = cdf( NaN, 1.0, 1.0 );
y = cdf( 0.0, NaN, 1.0 );
y = cdf( 0.0, 1.0, NaN );
If provided alpha <= 0
, the function returns NaN
.
var y = cdf( 2.0, -1.0, 0.5 );
y = cdf( 2.0, 0.0, 0.5 );
If provided beta <= 0
, the function returns NaN
.
var y = cdf( 2.0, 0.5, -1.0 );
y = cdf( 2.0, 0.5, 0.0 );
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 );
y = mycdf( 2.5 );
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.
License
See LICENSE.
Copyright
Copyright © 2016-2022. The Stdlib Authors.