A goodness of fit test for the exponential distribution

Abstract

In this paper we propose a new test statistic which is a modification of the Shapiro-Wilk W statistic for testing the goodness of fit for the exponential distribution. The test statistic is obtained by dividing the best linear unbiased estimate of the scale parameter by the probability weighted moment estimate of the same parameter. This ratio is both scale and location invariant and hence is an appropriate statistic for a test of the composite hypothsis of exponentiatily. The proposed test statistic is also modified for the case where the location parameter of the distribution is specified. Power comparisons are made by performing Monte Carlo experiments. It is shown that the suggested statistic is computationally simple and has good power properties. Some examples are given to illustrate test procedure.