README.md

Probability Density Function

Fréchet distribution probability density function.

The probability density function for a Fréchet random variable is

$$f\left( x; \mu, \beta \right ) = {\frac{\alpha }{s}}\;\left({\frac{x-m}{s}}\right)^{{-1-\alpha }}\;e^{{-({\frac{x-m}{s}})^{-\alpha}}}$$

where alpha > 0 is the shape, s > 0 the scale and m the location parameter.

Usage

var pdf = require( '@stdlib/stats/base/dists/frechet/pdf' );

pdf( x, alpha, s, m )

Evaluates the probability density function (PDF) for a Fréchet distribution with shape alpha, scale s, and location m at a value x.

var y = pdf( 10.0, 2.0, 3.0, 5.0 );
// returns ~0.1

y = pdf( -3.0, 1.0, 2.0, -4.0 );
// returns ~0.271

y = pdf( 0.0, 2.0, 1.0, -1.0 );
// returns ~0.736

If provided x <= m, the function returns 0.

var y = pdf( -2.0, 2.0, 1.0, -1.0 );
// returns 0.0

If provided NaN as any argument, the function returns NaN.

var y = pdf( NaN, 1.0, 1.0, 0.0 );
// returns NaN

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

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

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

If provided alpha <= 0, the function returns NaN.

var y = pdf( 2.0, -0.1, 1.0, 1.0 );
// returns NaN

y = pdf( 2.0, 0.0, 1.0, 1.0 );
// returns NaN

If provided s <= 0, the function returns NaN.

var y = pdf( 2.0, 1.0, -1.0, 1.0 );
// returns NaN

y = pdf( 2.0, 1.0, 0.0, 1.0 );
// returns NaN

pdf.factory( alpha, s, m )

Returns a function for evaluating the probability density function of a Fréchet distribution with shape alpha, scale s, and location m.

var mypdf = pdf.factory( 3.0, 3.0, 5.0 );

var y = mypdf( 10.0 );
// returns ~0.104

y = mypdf( 7.0 );
// returns ~0.173

Examples

var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/stats/base/dists/frechet/pdf' );

var alpha;
var m;
var s;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    alpha = randu() * 10.0;
    x = randu() * 10.0;
    s = randu() * 10.0;
    m = randu() * 10.0;
    y = pdf( x, alpha, s, m );
    console.log( 'x: %d, α: %d, s: %d, m: %d, f(x;α,s,m): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}

---

C APIs

Usage

#include "stdlib/stats/base/dists/frechet/pdf.h"

stdlib_base_dists_frechet_pdf( x, alpha, s, m )

Evaluates the probability density function (PDF) for a Fréchet distribution with shape alpha, scale s, and location m at a value x.

double y = stdlib_base_dists_frechet_pdf( 10.0, 2.0, 3.0, 2.0 );
// returns ~0.031

The function accepts the following arguments:

• x: [in] double input value.
• alpha: [in] double shape parameter.
• s: [in] double scale parameter.
• m: [in] double location parameter.

double stdlib_base_dists_frechet_pdf( const double x, const double alpha, const double s, const double m );

Examples

#include "stdlib/stats/base/dists/frechet/pdf.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 x;
    double s;
    double m;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        alpha = random_uniform( 0.0, 10.0 );
        s = random_uniform( 0.0, 10.0 );
        m = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_frechet_pdf( x, alpha, s, m );
        printf( "x: %lf, α: %lf, s: %lf, m: %lf, f(x;α,s,m): %lf\n", x, alpha, s, m, y );
    }
}