Derivation of the probability plot correlation coefficient test statistics for the generalized logistic and the generalized Pareto distributions

The selection of appropriate probability distribution is important in frequency analysis to estimate the accurate quantile. Generally, the selection of appropriate probability model is based on the goodness of fit test. The probability plot correlation coefficient (PPCC) test has been known as powerful and easy test among the goodness of fit tests. In this study, the derivation of the PPCC test statistics for the generalized logistic distribution and the generalized Pareto distribution was performed by considering sample sizes, significance levels, and shape parameters. In addition, the correlation coefficients between orderly generated data sets and fitted quantiles were computed by using various plotting position formulas. Monte Carlo simulation was performed to select an appropriate plotting position formula for assumed probability distributions. As the results, the Gringorten's plotting position formula was selected for given distributions. Finally, the PPCC test statistics for given probability distributions were derived from correlation coefficient values based on the selected plotting position formula considering various shape parameters.