Goodness-of-fit tests based on P-P probability plots

Abstract

Two goodness-of-fit statistics, based on measures of linearity for standardized P-P plots, are proposed and simple approximations for percentage points of these statistics are presented for testing the fit of exponential, Gumbel (Weibull), and normal (lognormal) probability models with unknown parameters. Results of extensive Monte Carlo power comparisons with other goodness-of-fit tests are summarized. The proposed tests are shown to have superior power for detecting light-tailed and moderate-tailed alternatives to the exponential distribution, but statistics based on measures of linearity for Q-Q plots tend to be more powerful against relatively heavy-tailed alternatives to hypothesized distributions with more moderate tails, such as the normal and Gumbel distributions.