Quantile Function

Weibull distribution quantile function.

The quantile function for a Weibull random variable is

for 0 <= p < 1, where lambda > 0 is the scale parameter and k > 0 is the shape parameter.

Installation

npm install @stdlib/stats-base-dists-weibull-quantile

Usage

var quantile = require( '@stdlib/stats-base-dists-weibull-quantile' );

quantile( p, k, lambda )

Evaluates the quantile function for a Weibull distribution with shape parameter k and scale parameter lambda.

var y = quantile( 0.5, 1.0, 1.0 );
// returns ~0.693

y = quantile( 0.2, 2.0, 4.0 );
// returns ~1.89

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( 0.0, NaN, 1.0 );
// returns NaN

y = quantile( 0.0, 1.0, NaN );
// returns NaN

If provided k <= 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 lambda <= 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( k, lambda )

Returns a function for evaluating the quantile function of a Weibull distribution with shape parameter k and scale parameter lambda.

var myquantile = quantile.factory( 2.0, 10.0 );

var y = myquantile( 0.2 );
// returns ~4.724

y = myquantile( 0.8 );
// returns ~12.686

Examples

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

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, 0.0, 10.0, opts );
var k = uniform( 10, 0.0, 10.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'p: %0.4f, k: %0.4f, λ: %0.4f, Q(p;k,λ): %0.4f', p, k, lambda, quantile );

C APIs

Usage

#include "stdlib/stats/base/dists/weibull/quantile.h"

stdlib_base_dists_weibull_quantile( p, k, lambda )

Evaluates the quantile function for a Weibull distribution with shape parameter k and scale parameter lambda.

double out = stdlib_base_dists_weibull_quantile( 0.5, 1.0, 1.0 );
// returns ~0.693

The function accepts the following arguments:

• p: [in] double input probability.
• k: [in] double shape parameter.
• lambda: [in] double scale parameter.

double stdlib_base_dists_weibull_quantile( const double p, const double k, const double lambda );

Examples

#include "stdlib/stats/base/dists/weibull/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 lambda;
    double p;
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        p = random_uniform( 0.0, 1.0 );
        k = random_uniform( 0.1, 5.0 );
        lambda = random_uniform( 0.1, 5.0 );
        y = stdlib_base_dists_weibull_quantile( p, k, lambda );
        printf( "p: %lf, k: %lf, λ: %lf, Q(p;k,λ): %lf\n", p, k, lambda, y );
    }
    return 0;
}

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.