Log-normal Distribution

Name

UxHwDoubleLognormalDist, UxHwFloatLognormalDist — Create a Log-normal distribution.

Synopsis

#include <uxhw.h>

double  UxHwDoubleLognormalDist(double mu, double sigma);
float   UxHwFloatLognormalDist(float mu, float sigma);

Description

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

$$f(x;\mu,\sigma)= \begin{cases} \frac{1}{x\sigma\sqrt{2\pi}}\exp\left[-\frac{\left(\ln x-\mu\right)^{2}}{2\sigma^{2}}\right] & x > 0,\\ 0 & x\le 0. \end{cases}$$

Parameters

• mu $\in (-\infty, \infty)$ — The logarithm of the scale parameter ($\mu$).
• sigma $\in [0, \infty)$ — The standard deviation ($\sigma$) of the underlying normal distribution.

Return Values

The UxHwDoubleLognormalDist() function returns the mean of samples of a Log-normal distribution with parameters mu and sigma. If sigma < 0, the function returns NaN.

✏️   Examples

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

int
main(void)
{
    double  value = UxHwDoubleLognormalDist(0.0, 1.0);
    printf("value = %lf\n", value);

    return 0;
}