A Test of Exponentiality Based on Spacings for Progressively Type-II Censored Data

There have been numerous tests proposed in the literature to determine whether or not an exponential model is appropriate for a given data set. These procedures range from graphical techniques, to tests that exploit characterization results for the exponential distribution. In this article, we propose a goodness-of-fit test for the exponential distribution based on general progressively Type-II censored data. This test based on spacings generalizes a test proposed by Tiku (1980). We derive the exact and asymptotic null distribution of the test statistic. The results of a simulation study of the power under several different alternatives like the Weibull, Lomax, Lognormal and Gamma distributions are presented. We also discuss an approximation to the power based on normality and compare the results with those obtained by simulation. A wide range of sample sized and progressive censoring schemes have been considered for the empirical study. We also compare the performance of this procedure with two standard tests for exponentiality, viz. the Cramer-von Mises and the Shapiro-Wilk test. The results are illustrated on some real data for the one-and two-parameter exponential models. Finally, some extensions to the multi-sample case are suggested.