The Probability Plot Correlation Coefficient Test for the Normal, Lognormal, and Gumbel Distributional Hypotheses

Abstract

Filliben (1975) and Looney and Gulledge (1985) developed powerful tests of normality which are conceptually simple and computationally convenient and may be readily extended to testing nonnormal distributional hypotheses. The probability plot correlation coefficient test consists of two widely used tools in water resource engineering: the probability plot and the product moment correlation coefficient. Many water resource applications require powerful hypothesis tests for nonnormal distributions. This technical note develops a new probability plot correlation coefficient test for the Gumbel distribution. Critical points of the test statistic are provided for samples of length 10 to 10,000. Filliben's and Looney and Gulledge's tests were originally developed for testing the normal hypothesis for sample sizes less than 100. Since many water resource research applications require a test of normality for samples of length greater than 100, Filliben's test is extended here for samples of length 100 to 10,000.