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On the distribution of the ratio of two random variables having generalized life distributions. (English) Zbl 0217.51002

Summary: M. Zelen and M. C. Dannemiller [Technometrics 3, 29–49 (1961; Zbl 0109.37503)] proposed a general life distribution function using a weighted sum of Laguerre polynomials (with non-constant weights). Their results are extended here by obtaining the distribution of the ratio of two random variables having this general life distribution. This result is used to examine the robustness of the two-sample exponential likelihood ratio test for comparing means. The test is found to be markedly nonrobust.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62N05 Reliability and life testing
62E15 Exact distribution theory in statistics
62F03 Parametric hypothesis testing

Citations:

Zbl 0109.37503
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