Much work has been done on the extreme value distribution for the most extreme value, either maximum or minimum. In many cases because of economic or other considerations the best plan is not to design for the most extreme weather event. The mth extreme value is a rational design variable in such instances (Thom, 1969).

The density function for the mth extreme value of the variable x is 
f(x) = mm{exp[−m(xαm)/βmm exp − (xαm/βm]}/βm(m − 1)!,
where αm and βm are the parameters of the distribution. The method of maximum likelihood is used to find expressions for estimating these parameters. These two expressions are solved using the Newton-Raphson method for samples of temperature data.

The Kolmogorov-Smirnov statistic for goodness-of-fit is calculated for each sample. The tables of critical values for testing the level of significance of the test statistic are not applicable since the parameters are estimated from the sample. Tables of critical values for the Kolmogorov-Smirnov statistic for testing the goodness-of-fit of the most extreme value distribution when the BLI estimator for the parameters have previously been developed. Tables of critical values of the Kolmogorov-Smirnov statistic for the mth extreme value (m = 1, 2, …, 12) from a normal parent distribution are developed from Monte Carlo simulations.

This content is only available as a PDF.