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

$$f(x;\mu,\beta)=\frac{e^{-z+e^{-z}}}{\beta},\quad z=\frac{x-\mu}{\beta}.$$

Parameters

• mu — The location parameter ($\mu$) of the Gumbel-1 distribution.
• beta — The scale parameter ($\beta$) 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;
}