Gumbel distribution skewness.
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[Gumbel][gumbel-distribution] distribution [skewness][skewness].
μ and scale β ismath
\mathop{\mathrm{skew}}\left( X \right) = {\frac{12{\sqrt{6}}\,\zeta(3)}{\pi^{3}}} \approx 1.14ζ is the [Riemann zeta function][zeta].bash
npm install @stdlib/stats-base-dists-gumbel-skewnessscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var skewness = require( '@stdlib/stats-base-dists-gumbel-skewness' );mu and scale parameter beta.javascript
var y = skewness( 2.0, 1.0 );
// returns ~1.14
y = skewness( 0.0, 1.0 );
// returns ~1.14
y = skewness( -1.0, 4.0 );
// returns ~1.14NaN as any argument, the function returns NaN.javascript
var y = skewness( NaN, 1.0 );
// returns NaN
y = skewness( 0.0, NaN );
// returns NaNbeta <= 0, the function returns NaN.javascript
var y = skewness( 0.0, 0.0 );
// returns NaN
y = skewness( 0.0, -1.0 );
// returns NaNjavascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var skewness = require( '@stdlib/stats-base-dists-gumbel-skewness' );
var opts = {
'dtype': 'float64'
};
var beta = uniform( 10, 0.0, 10.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
logEachMap( 'µ: %0.4f, β: %0.4f, skew(X;µ,β): %0.4f', mu, beta, skewness );c
#include "stdlib/stats/base/dists/gumbel/skewness.h"mu and scale beta.c
double y = stdlib_base_dists_gumbel_skewness( 0.0, 1.0 );
// returns ~1.14[in] double location parameter.[in] double scale parameter.c
double stdlib_base_dists_gumbel_skewness( const double mu, const double beta );c
#include "stdlib/stats/base/dists/gumbel/skewness.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 beta;
double mu;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
mu = random_uniform( -5.0, 5.0 );
beta = random_uniform( 0.0, 20.0 );
y = stdlib_base_dists_gumbel_skewness( mu, beta );
printf( "µ: %lf, β: %lf, Skew(X;µ,β): %lf\n", mu, beta, y );
s}
}
