Bounded Pareto Distribution

Name

UxHwDoubleBoundedparetoDist, UxHwFloatBoundedparetoDist — Create a Bounded Pareto distribution.

Synopsis

#include <uxhw.h>

double  UxHwDoubleBoundedparetoDist(double alpha, double xMin, double xMax);
float   UxHwFloatBoundedparetoDist(float alpha, float xMin, float xMax);

Description

The UxHwDoubleBoundedparetoDist() function, on architectures that associate distributional information with floating-point values, creates a Bounded Pareto distribution with parameters alpha, xMin, and xMax and associates it with its return value. The particle return value is the mean value of a Bounded Pareto distribution with parameters alpha, xMin, and xMax. The probability density function of the bounded Pareto distribution is

$$f(x;\alpha,x_{\min},x_{\max})=\begin{cases} \frac{x_{\max}^\alpha}{x_{\max}^\alpha-x_{\min}^\alpha} \frac{\alpha x_{\min}^\alpha }{x^{\alpha+1}} & x_{\min} \le x \le x_{\max} \\ 0 & \text{otherwise.} \end{cases}$$

Parameters

• alpha — The shape parameter ($\alpha$).
• xMin — The minimum of the distribution support ($x_{\min}$).
• xMax — The maximum of the distribution support ($x_{\max}$).

Return Values

The UxHwDoubleBoundedparetoDist function returns the mean of samples of a Bounded Pareto distribution with parameters alpha, xMin and xMax. If alpha <= 0, xMin <= 0, or xMin > xMax, the function returns NaN.

✏️   Examples

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

int
main(void)
{
    double  value = UxHwDoubleBoundedparetoDist(1.0, 0.5, 10.0);
    printf("value = %lf\n", value);

    return 0;
}