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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.
import pdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-pdf@esm/index.mjs';
You can also import the following named exports from the package:
import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-pdf@esm/index.mjs';
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
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
<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import pdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-pdf@esm/index.mjs';
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 ) );
}
</script>
</body>
</html>
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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.