Cumulative Distribution Function

Fréchet distribution cumulative distribution function.

The cumulative distribution function for a Fréchet random variable is

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

Installation

npm install @stdlib/stats-base-dists-frechet-cdf

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_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 );
    }
}

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.