Skewness

Fréchet distribution skewness.

The skewness for a Fréchet random variable shape α > 0, scale s > 0, and location parameter m is

where Γ is the gamma function.

Usage

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

skewness( alpha, s, m )

Returns the skewness for a Fréchet distribution with shape alpha > 0, scale s > 0, and location parameter m.

var y = skewness( 4.0, 1.0, 1.0 );
// returns ~5.605

y = skewness( 4.0, 8.0, -3.0 );
// returns ~5.605

y = skewness( 5.0, 1.0, 2.0 );
// returns ~3.535

If 0 < alpha <= 3, the function returns +Infinity.

var y = skewness( 2.5, 1.0, 1.0 );
// returns Infinity

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

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

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

y = skewness( 1.0, 1.0, NaN );
// returns NaN

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

var y = skewness( 0.0, 3.0, 2.0 );
// returns NaN

y = skewness( -1.0, 3.0, 2.0 );
// returns NaN

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

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

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

Examples

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

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

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*20.0 ) + EPS;
    s = ( randu()*20.0 ) + EPS;
    m = ( randu()*40.0 ) - 20.0;
    y = skewness( alpha, s, m );
    console.log( 'α: %d, s: %d, m: %d, skew(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_frechet_skewness( alpha, s, m )

Returns the skewness for a Fréchet distribution with shape alpha, scale s, and location m.

double y = stdlib_base_frechet_skewness( 5.0, 2.0, 0.0 );
// returns ~3.535

The function accepts the following arguments:

alpha: [in] double shape parameter.
s: [in] double scale parameter.
m: [in] double location parameter.

double stdlib_base_dists_frechet_skewness( const double alpha, const double s, const double m );

Examples

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

    for ( i = 0; i < 10; i++ ) {
       alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
       s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
       m = random_uniform( -20.0, 20.0 );
       y = stdlib_base_dists_frechet_skewness( alpha, s, m );
       printf( "α: %.4lf, s: %.4lf, m: %.4lf, skew(X;α,s,m): %.4lf\n", alpha, s, m, y );
    }
}