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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var quantile = require( '@stdlib/stats-base-dists-pareto-type1-quantile' );

var opts = {
    'dtype': 'float64'
};
var alpha = uniform( 10, 0.0, 5.0, opts );
var beta = uniform( 10, 0.0, 5.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'p: %0.4f, α: %0.4f, β: %0.4f, Q(p;α,β): %0.4f', p, alpha, beta, quantile );

C APIs

Usage

#include "stdlib/stats/base/dists/pareto-type1/quantile.h"

stdlib_base_dists_pareto_type1_quantile( p, alpha, beta )

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

double y = stdlib_base_dists_pareto_type1_quantile( 0.8, 2.0, 1.0 );
// returns ~2.236

The function accepts the following arguments:

• p: [in] double input probability.
• alpha: [in] double shape parameter.
• beta: [in] double scale parameter.

double stdlib_base_dists_pareto_type1_quantile( const double p, const double alpha, const double beta );

Examples

#include "stdlib/stats/base/dists/pareto-type1/quantile.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double alpha;
    double beta;
    double p;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        alpha = random_uniform( 1.0, 10.0 );
        beta = random_uniform( 1.0, 10.0 );
        y = stdlib_base_dists_pareto_type1_quantile( p, alpha, beta );
        printf( "p: %lf, α: %lf, β: %lf, Q(p;α,β): %lf\n", p, alpha, beta, y );
    }
}

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 © 2016-2026. The Stdlib Authors.