Gamma Distribution

Name

UxHwDoubleGammaDist, UxHwFloatGammaDist — Create a Gamma distribution.

Synopsis

#include <uxhw.h>

double	UxHwDoubleGammaDist(double k, double theta);
float	UxHwFloatGammaDist(float k, float theta);

Description

The UxHwDoubleGammaDist() function, on architectures that associate distributional information with floating-point values, creates a Gamma distribution with parameters k and theta and associates it with its return value. The particle return value is the mean value of a Gamma distribution with parameters k and theta. The probability density function of the Gamma distribution is

$$\begin{cases} \frac{1}{\Gamma(k)\theta^k}x^{k-1}e^{-x/\theta} & x>0, \\ 0 & x \le 0. \end{cases}$$

Parameters

• k $\in (0, \infty)$ — The shape parameter ($k$) of the Gamma distribution.
• theta $\in [0, \infty)$ — The scale parameter ($\theta$) of the Gamma distribution.

Return values

The UxHwDoubleGammaDist() function returns the mean value of a Gamma distribution with parameters k and theta and associates it with a Gamma distribution with parameters k and theta. If theta = 0 and k > 0, the function returns $0$.

Illegal parameter values

If k <= 0 or theta < 0, the function returns NaN. If k or theta is NaN, the function returns -NaN. See Handling of NaN.

Examples

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

int
main(void)
{
  double	value = UxHwDoubleGammaDist(1.0, 3.0);
  printf("value = %lf\n", value);

  return 0;
}