Nth Centralized Moment of a Distribution

Name

UxHwDoubleNthMoment, UxHwFloatNthMoment — Return the nth centralized moment of a distribution.

Synopsis

#include <stddef.h>
#include <uxhw.h>

double  UxHwDoubleNthMoment(double value, size_t n);
float   UxHwFloatNthMoment(float value, size_t n);

Description

The UxHwDoubleNthMoment() function returns the $n$th centralized moment of the distribution associated with value, on architectures that associate distributional information with floating-point values. The $n$th centralized moment of a distribution, in statistics is given by $E((X - \mu)^n)$, where $\mu$ is the mean of the distribution and $n$ is the order of the moment. The second centralized moment of a distribution is its variance, which is the square of its standard deviation ($\sigma$). Because the first centralized moment of a distribution is by definition zero, for n equal to one the UxHwDoubleNthMoment() function returns the mean value of the distribution associated with value.

Parameters

• value — The distributional value to calculate the centralised moment from.
• n — The order of the centralized moment.

Return Values

The UxHwDoubleNthMoment() function returns the $n$th centralized moment of the distribution value, if n != 1. The UxHwDoubleNthMoment() function returns the mean value of the distribution value, if n == 1.

If n == 0, the function returns 1. If there is no distribution associated with value and n == 1, the function returns value. If there is no distribution associated with value and n > 1, the function returns 0.

✏️   Examples

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

int
main(void)
{
    double  a = UxHwDoubleUniformDist(10.0, 20.0);
    double  secondMoment = UxHwDoubleNthMoment(a, 2);
    double  meanValue = UxHwDoubleNthMoment(a, 1);

    printf("Second centralized moment is %lf\n", secondMoment);
    printf("Mean value is %lf\n", meanValue);

    return 0;
}