README.md

Cumulative Distribution Function

Fréchet distribution cumulative distribution function.

The cumulative distribution function for a Fréchet random variable is

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

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

Usage

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

cdf( x, alpha, s, m )

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

var y = cdf( 10.0, 2.0, 3.0, 5.0 );
// returns ~0.698

y = cdf( -3.0, 1.0, 2.0, -4.0 );
// returns ~0.135

y = cdf( 0.0, 2.0, 1.0, -1.0 );
// returns ~0.368

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

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

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

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

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

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

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

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

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

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

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

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

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

cdf.factory( alpha, s, m )

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

var mycdf = cdf.factory( 3.0, 3.0, 5.0 );

var y = mycdf( 10.0 );
// returns ~0.806

y = mycdf( 7.0 );
// returns ~0.034

Examples

var uniform = require( '@stdlib/random/base/uniform' );
var EPS = require( '@stdlib/constants/float64/eps' );
var cdf = require( '@stdlib/stats/base/dists/frechet/cdf' );

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

for ( i = 0; i < 100; i++ ) {
    alpha = uniform( EPS, 5.0 );
    s = uniform( EPS, 5.0 );
    m = uniform( -2.0, 2.0 );
    x = uniform( m + 0.1, m + 10.0 );
    y = cdf( 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/cdf.h"

stdlib_base_dists_frechet_cdf( x, alpha, s, m )

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

double y = stdlib_base_dists_frechet_cdf( 10.0, 2.0, 3.0, 2.0 );
// returns ~0.869

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

Examples

#include "stdlib/stats/base/dists/frechet/cdf.h"
#include "stdlib/constants/float64/eps.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++ ) {
        alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
        m = random_uniform( -2.0, 2.0 );
        x = random_uniform( m + 0.1, m + 10.0 );
        y = stdlib_base_dists_frechet_cdf( 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 );
    }
}