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Gumbel-1 Distribution

Name​

UxHwDoubleGumbel1Dist, UxHwFloatGumbel1Dist — Create a Gumbel-1 distribution.

Synopsis​

#include <uxhw.h>

double  UxHwDoubleGumbel1Dist(double mu, double beta);
float   UxHwFloatGumbel1Dist(float mu, float beta);

Description​

The UxHwDoubleGumbel1Dist() function, on architectures that associate distributional information with floating-point values, creates a Gumbel-1 distribution with parameters mu and beta and associates it with its return value. The particle return value is the mean of a Gumbel-1 distribution with parameters mu and beta. The probability density function of the Gumbel-1 distribution is

f(x;μ,β)=e−z+e−zβ,z=x−μβ.f(x;\mu,\beta)=\frac{e^{-z+e^{-z}}}{\beta},\quad z=\frac{x-\mu}{\beta}.

Parameters​

  • mu — The location parameter (μ\mu) of the Gumbel-1 distribution.
  • beta — The scale parameter (β\beta) of the Gumbel-1 distribution.

Return Values​

The UxHwDoubleGumbel1Dist() function returns the mean of samples of a Gumbel-1 distribution with parameters mu and beta. If beta < 0, the function returns NaN.

✏️   Examples​

#include <stdio.h>
#include <uxhw.h>

int
main(void)
{
    double  value = UxHwDoubleGumbel1Dist(1.0, 2.0);
    printf("value = %lf\n", value);

    return 0;
}