A new class of tests for exponentiality

The purpose of this study is to investigate a new class of tests for exponentiality versus broad alternatives. In Chapter 1, a selection of tests for exponentiality against broad alternatives are reviewed. The null cumulative distribution of the test statistic, T_r,s, as well as its null mean and null variance are developed in Chapter 2. Also, in Chapter 2, a table of the null cumulative distribution function for selected values is provided. In Chapter 3 very easily applied asymptotic distributions for the test statistic are derived. The power of the test proposed in Chapter 2 is investigated in Chapter 4. Two small Monte Carlo studies are used to estimate the power of test versus Weibull alternatives with shape parameters 2 and 1/2 . Also, the test T_r,s is compared with another test for exponentiality. Finally, the exact value and the asymptotic value of the null cumulative distribution function of T_1,5 with sample 5, F_5,1,5 compared to give some intuitive feel of the preciseness of the asymptotic distribution.

It is found that the test proposed has considerable power against DFR alternatives and compares well against at least one alternate test for exponentiality. Also, the asymptotic distributions, even with the small sample size of 5 are very accurate.