Testing equality of means and variances of several Weibull populations

The usual practice for testing homogeneity of several populations in terms of means and variances is first to test for the equality of variances and once this assumption is found to be tenable then to test the equality of means. Singh (1986) proposes a very interesting procedure based on two likelihood ratio statistics for testing homogeneity of several normal (μ, σ) populations. Singh uses a method by Fisher (1950) which is based on combining two or more independent tests. Paul and Jiang (2004) generalized Fisher’s method for testing homogeneity of several two-parameter populations based on two asymptotically independent likelihood ratio and two asymptotically independent score test statistics. They then obtained specific results to test homogeneity of several normal, several negative binomial and several beta-binomial populations. Based on simulations from these populations they show that Fisher’s method of combining two statistics, even when they are only asymptotically independent, does, in general, perform well for testing homogeneity of several two-parameter populations. However, the score test statistics have simple forms, easy to calculate, and have uniformly good level properties. Therefore they recommend Fisher’s method based on combining two score test statistics. Note that their conclusion is based on simulation results for the normal and two discrete populations. The purpose of this paper is to investigate the performance of Fisher’s method for testing homogeneity of several Weibull populations.