RECENT PROBABILITY RESULTS FOR EXTREME AGES.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Consider a very large number of persons, and probability distributions for the age at death of the last survivor, next to last survivor, etc. First, suppose that the persons are statistically independent with the same probability distribution for age at death random sample case. Then, some approximations to distributions of extremes are often usable. These approximations are completely specified except for at most three parameters. This simplifies distribution estimation to estimation of the parameters. Moreover, previous large samples possibly different sizes from the same population of persons, and much of their data on extremes, can be used for estimation. Also, the sample results often remain applicable for the more general case of independence or mild dependence but possibly different distributions for the ages at death. Here, the average of these distributions is sampled. Very recent results show that distributions of extremes are of the sample type for any joint distribution of the ages at death. However, the distribution sampled can be greatly different for the last survivor, next to last survivor, etc. This effectively limits estimation of parameters to previous groups having very nearly the same joint distribution and use of one observed extreme per group. Author
- Statistics and Probability