k3: The third central moment

In dangulod/ECTools: Economic Capital Tools

Description

The third central moment

Usage

k3(x)

Arguments

loss	vector with input
scale	scale parameter

Value

The third central moment is the measure of the lopsidedness of the distribution; any symmetric distribution will have a third central moment, if defined, of zero. The normalised third central moment is called the skewness, often Gamma. A distribution that is skewed to the left (the tail of the distribution is longer on the left) will have a negative skewness. A distribution that is skewed to the right (the tail of the distribution is longer on the right), will have a positive skewness. For distributions that are not too different from the normal distribution, the median will be somewhere near MU <e2><88><92> Gamma * Sigma / 6; the mode about MU <e2><88><92> Gamma * Sigma / 2.

References

https://en.wikipedia.org/wiki/Moment_(mathematics)

dangulod/ECTools documentation built on May 4, 2019, 3:19 p.m.