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@stdlib/stats-base-dists-pareto-type1-cdf
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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.
npm install @stdlib/stats-base-dists-pareto-type1-cdf
var cdf = require( '@stdlib/stats-base-dists-pareto-type1-cdf' );
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
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
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 ) );
}
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.
See LICENSE.
Copyright © 2016-2021. The Stdlib Authors.
FAQs
Pareto (Type I) distribution cumulative distribution function (CDF).
We found that @stdlib/stats-base-dists-pareto-type1-cdf demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 4 open source maintainers collaborating on the project.
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