@stdlib/stats-base-dists-pareto-type1-quantile
v0.2.1
Published
Pareto (Type I) distribution quantile function.
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Quantile Function
Pareto (Type I) distribution quantile function.
The quantile function for a Pareto (Type I) random variable is
for 0 <= p < 1
, where alpha
is the shape parameter and beta
is the scale parameter.
Installation
npm install @stdlib/stats-base-dists-pareto-type1-quantile
Usage
var quantile = require( '@stdlib/stats-base-dists-pareto-type1-quantile' );
quantile( p, alpha, beta )
Evaluates the quantile function for a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
( scale parameter).
var y = quantile( 0.8, 2.0, 1.0 );
// returns ~2.236
y = quantile( 0.8, 1.0, 10.0 );
// returns ~50.0
y = quantile( 0.1, 1.0, 10.0 );
// returns ~11.111
If provided a probability p
outside the interval [0,1]
, the function returns NaN
.
var y = quantile( 1.9, 1.0, 1.0 );
// returns NaN
y = quantile( -0.1, 1.0, 1.0 );
// returns NaN
If provided NaN
as any argument, the function returns NaN
.
var y = quantile( NaN, 1.0, 1.0 );
// returns NaN
y = quantile( 0.5, NaN, 1.0 );
// returns NaN
y = quantile( 0.5, 1.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var y = quantile( 0.4, -1.0, 1.0 );
// returns NaN
y = quantile( 0.4, 0.0, 1.0 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = quantile( 0.4, 1.0, -1.0 );
// returns NaN
y = quantile( 0.4, 1.0, 0.0 );
// returns NaN
quantile.factory( alpha, beta )
Returns a function for evaluating the quantile function of a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
( scale parameter).
var myquantile = quantile.factory( 2.5, 0.5 );
var y = myquantile( 0.5 );
// returns ~0.66
y = myquantile( 0.8 );
// returns ~0.952
Examples
var randu = require( '@stdlib/random-base-randu' );
var quantile = require( '@stdlib/stats-base-dists-pareto-type1-quantile' );
var alpha;
var beta;
var p;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
p = randu();
alpha = randu() * 5.0;
beta = randu() * 5.0;
y = quantile( p, alpha, beta );
console.log( 'p: %d, α: %d, β: %d, Q(p;α,β): %d', p.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.