F-distribution

Name

UxHwDoubleFDist, UxHwFloatFDist — Create an F-distribution.

Synopsis

#include <uxhw.h>

double	UxHwDoubleFDist(double d1, double d2);
float	UxHwFloatFDist(float d1, float d2);

Description

The UxHwDoubleFDist() function, on architectures that associate distributional information with floating-point values, creates an F distribution with parameters d1 and d2 and associates it with its return value. The particle return value is the mean value of an F-distribution with parameters d1 and d2. The probability density function of the F-distribution is

$$\begin{cases} f(x) = \frac{1}{B\left(\frac{d_1}{2},\frac{d_2}{2}\right)} \left(\frac{d_1}{d_2}\right)^{\frac{d_1}{2}} x^{\frac{d_1}{2} - 1} \left(1+\frac{d_1}{d_2} \, x \right)^{-\frac{d_1+d_2}{2}} & x\ge 0, \\ 0 & x < 0. \end{cases}$$

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

Parameters

• d1 — The parameter ($d_1$) of the F-distribution.
• d2 — The parameter ($d_2$) of the F-distribution.

Return Values

The UxHwDoubleFDist() function returns the mean of samples of a F-distribution with parameters d1 and d2. If d1<=0or d2<=2, the function returns NaN.

✏️   Examples

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

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

	return 0;
}