Derivation of the Probability Plot Correlation Coefficient Test Statistics for the General Extreme Value Distribution

An appropriate probability distribution for estimating an accurate quantile is selected by the goodness of fit test in frequency analysis. Among the goodness of fit tests, the PPCC(probability plot correlation coefficient) test has been known as powerful test. Generally, the PPCC test statistics are influenced by significance levels, sample sizes, plotting position formulas, and shape parameters(in case that a given distribution includes a shape parameter). It is important to select an exact plotting position formula because the PPCC test statistics for given probability distributions are derived from correlation coefficient values based on the selected plotting position formula. After Cunnane(1978) defined the plotting position that related with the mean of data, various plotting position formulas have been developed for considering the effect of coefficients of skewness related with shape parameters. In this study, the PPCC test statistics are derived by using a plotting position formula contained a term of a coefficient of skewness for the GEV(general extreme value) distribution. In addition, the derivation of the PPCC test statistics is performed by considering various sample sizes, significance levels, and shape parameters of the GEV distribution.