Tests of exponentiality against some parametric over/under-dispersed life time models

Abstract

We develop tests of goodness of fit of the exponential model against some over/under dispersion family of distributions. In particular, we develop 3 score test statistics and 3 likelihood ratio statistics. These are (S₁, L₁), (S₂, L₂), and (S₃, L₃) based on a general over-dispersed family of distributions, two specic over/under dispersed exponential models, namely, the gamma and the Weibull distributions, respectively. A simulation study shows that the statistics S₃ and L₃ have best overall performance, in terms of both, level and power. However, the statistic L₃ can be liberal in some instances and it needs the maximum likelihood estimates of the parameters of the Weibull distribution as opposed to the statistic S₃ which is very simple to use. So, our recommendation is to use the statistic S₃ to test the fit of an exponential distribution over any over/under-dispersed exponential distribution.