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RESULTS ON STATISTICAL ESTIMATION AND HYPOTHESIS TESTING WITH APPLICATION TO THE WEIBULL AND EXTREME-VALUE DISTRIBUTIONS,
ROCKETDYNE CANOGA PARK CALIF
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The report consists of four distinct papers which are related by the fact that all apply to the first asymptotic distribution of smallest extreme values or, equivalently, the two-parameter Weibull distribution. The first paper considers a life-testing situation in which one or more sample items may be removed from test at the time of any failure, and in which the population of failure times from which the sample is randomly selected for the life test has a two-parameter Weibull distribution. The fourth paper gives tables for obtaining exact lower confidence on reliable life under the same Weibull assumption for failure time, but applies only to cases in which the number of items removed at the time of any failure consists of all the survivors. The second paper considers two populations, each of which has a first asymptotic distribution of smallest values. A test is derived for testing the hypothesis that the scale parameters of the two populations are equal. Critical values of the test statistic are calculated and tabulated for one confidence level and for singly censored independent samples, sizes 2 through 6, from the two populations. In the third paper are tables of expected-value and covariance matrices of reduced order statistics from the first asymptotic distribution of smallest values for sample sizes 1 through 25. Author
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