Logarithm of Cumulative Distribution Function

Fréchet distribution logarithm of 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-logcdf

Usage

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

logcdf( x, alpha, s, m )

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

var y = logcdf( 10.0, 2.0, 3.0, 5.0 );
// returns ~-0.36

y = logcdf( -3.4, 1.0, 2.0, -4.0 );
// returns ~-3.333

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

If provided x <= m, the function returns -Infinity.

var y = logcdf( -2.0, 2.0, 1.0, -1.0 );
// returns -Infinity

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

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

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

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

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

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

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

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

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

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

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

logcdf.factory( alpha, s, m )

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

var mylogcdf = logcdf.factory( 3.0, 3.0, 5.0 );

var y = mylogcdf( 10.0 );
// returns ~-0.216

y = mylogcdf( 7.0 );
// returns ~-3.375

Notes

• In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

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

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 = logcdf( x, alpha, s, m );
    console.log( 'x: %d, α: %d, s: %d, m: %d, ln(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/logcdf.h"

stdlib_base_dists_frechet_logcdf( x, alpha, s, m )

Evaluates the natural logarithm of 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_logcdf( 10.0, 2.0, 3.0, 2.0 );
// returns ~-0.141

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

Examples

#include "stdlib/stats/base/dists/frechet/logcdf.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( 0.0, 10.0 );
        x = 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_logcdf( x, alpha, s, m );
        printf( "x: %lf, α: %lf, s: %lf, m: %lf, ln(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.