README.md

Quantile Function

Weibull distribution quantile function.

The quantile function for a Weibull random variable is

$$Q(p;k,\lambda) = \lambda {(-\ln(1-p))}^{1/k}$$

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

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

var lambda;
var k;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    lambda = randu() * 10.0;
    k = randu() * 10.0;
    y = quantile( p, k, lambda );
    console.log( 'p: %d, k: %d, λ: %d, Q(p;k,λ): %d', p, k, lambda, y );
}

---

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 p;
    double k;
    double lambda;
    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, lambda: %lf, Q(p;k,lambda): %lf\n", p, k, lambda, y );
    }
    return 0;
}