Contents
- Index
Largest Extreme Value Family of Distributions
Shape:
The largest extreme value family of distributions is made up of three distributions: Fréchet, negative Weibull and largest extreme value. It covers any specified average, standard deviation and any skewness below 5.6051382. Together they form a 3-parameter family of distributions that is represented by a curve on a skewness-kurtosis plot as shown below. The Fréchet distribution covers the portion of the curve with skewness above 1.139547. The negative Weibull distribution covers the portion of the curve with skewness below 1.139547. The largest extreme value distribution handles the remaining case of skewness equal to 1.139547.
Density Function - Largest Extreme Value Distribution:
The density function of the largest extreme value distribution is shown below:
The equation, parameters and bounds of the density function are:
Moments - Largest Extreme Value Distribution:
The moments of the largest extreme value distribution can be calculated from the parameters as shown below:
Density Function - Fréchet:
The density function of the Fréchet distribution is shown below:
The equation, parameters and bounds of the density function are:
Moments - Fréchet:
The moments of the Fréchet distribution can be calculated from the parameters as shown below:
Properties:
The negative exponential distribution is a special case of the negative Weibull distribution and thus falls on the negative Weibull curve in the skewness-kurtosis plot.
The negative Weibull and largest extreme value distributions are the distributions of maximums. Under certain restrictions, the maximum of distributions without upper bounds tends to the largest extreme value distribution and the maximum of distributions bounded above tends to the negative Weibull.