Beta Distribution

Name

UxHwDoubleBetaDist, UxHwFloatBetaDist — Create a Beta distribution.

Synopsis

#include <uxhw.h>

double	UxHwDoubleBetaDist(double a, double b);
float	UxHwFloatBetaDist(float a, float b);

Description

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

$$\begin{cases} \frac{x^{a-1} (1-x)^{b-1}}{B(a,b)} & x\in [0,1], \\ 0 & \mathrm{else}. \end{cases}$$

where $B(a,b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$ is the Beta function and $\Gamma$ is the Gamma function.

Parameters

• a $\in (0, \infty)$ — The shape parameter ($a$) of the Beta distribution.
• b $\in (0, \infty)$ — The shape parameter ($b$) of the Beta distribution.

Return values

The UxHwDoubleBetaDist() function returns the mean value of a Beta distribution with parameters a and b and associates it with a Beta distribution with parameters a and b.

Illegal parameter values

If a <= 0 or b <= 0, the function returns NaN. If a or b is NaN or INFINITY, the function returns -NaN. See Handling of NaN.

Examples

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

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

  return 0;
}