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AbstractA class of exponential type distributions with special exponential parameters is defined. It is assumed that the exponential parameters vary according to some (known) probability law. It has been shown in this paper that the compound distribution can be easily represented in form involving moment generating function of the mixing distribution. The results obtained in this paper provide an efficient and simple method of obtaining compound failure time distribution with known mixing distributions (uniform, exponential, gamma).

Summary  The known results of optimal allocation in two‐stage simple random sampling with stratification from finite population are generalized for J‐stages. The optimalization is treated by minimizing the cost function for given variance as well as by minimizing the variance for given cost. It turns out that for both cases the optimal values differ only for the first‐stage units and are the same for all the subsequent. The general formula for minimum variance of the unbiased estimator of the population mean per element is given.

Part I: Survival measurements and concepts -- 1. Survival data -- 2. Measures of mortality and morbidity, ratios, proportions, and means -- 3. Survival distributions -- Part II: Mortality experiences and life tables -- 4. Life tables: fundamentals and construction -- 5. Complete mortality data, estimation of survival function -- 6. Incomplete mortality data: follow-up studies -- 7. Fitting parametric survival distributions -- 8. Comparison of mortality experiences -- 9. Theory of competing causes: probabilistic approach -- 10. Multiple decrement life tables -- 1. Single decrement life tables associated with multiple decrement life tables: their interpretation and meaning -- 12. Estimation and testing hypotheses in competing risk analysis -- Part IV: Some more advanced topics -- 13. Concomitant variables in lifetime distributions models -- 14. Age of onset distributions -- 15. Models of aging and chronic diseases.