Regression equations of probability plot correlation coefficient test statistics from several probability distributions

The probability plot correlation coefficient (PPCC) test has been known as a powerful but easy-to-use goodness-of-fit test. However, the application of PPCC test statistics is sometimes difficult since the test statistics are generally derived in tabulated form and the number of test statistics is significant. In this study, the PPCC test statistics for the normal, Gumbel, gamma, GEV, and Weibull distributions are derived, and regression equations of the PPCC test statistics for those models are formulated as a function of the significance levels, sample sizes, and skewness coefficients depending on the models. Monte Carlo simulation for power tests were performed to compare the rejection capability of the PPCC test with those of the χ², Cramer von Mises, and Kolmogorov-Smirnov tests for several probability distributions. The power test results indicated that the PPCC and χ²-tests had better rejection performances than the CVM and K-S tests did when the parent and applied models were identical. Moreover, the PPCC test showed the most powerful rejection rate, followed by the χ²-test, while the CVM was the worst when the parent and applied models were different. In addition, the power of rejection increased with sample size when the parent and applied models were different. However, the rejection power did not vary appreciably with sample size when the parent and applied models were identical.