| Summary: | 碩士 === 淡江大學 === 統計學系 === 90 === In this paper, we discuss the lifetime of a product from the new two parameter distribution with the bathtub shape or increasing failure rate function by doubly typeⅡcensored samples and upper record values. First, we provide ten pivotal quantities to test the shape parameter of the new two parameter distribution and establish confidence interval of the shape parameter in typeⅡcensored samples. Second, we extend typeⅡcensored samples to upper record values. Similarly, we will provide several pivotal quantities and to test hypotheses and establish the confidence interval of the shape parameter. This paper proposes a simple exact statistical test for the shape parameter of the new two parameter distribution, as well as an exact confidence interval for the same parameter by typeⅡcensored samples and upper record values. Necessary critical values of the test are given. Finally, we give some examples and the Monte Carlo simulation to assess the behavior（including higher power and more shorter length of confidence interval）of these pivotal quantities for testing null hypotheses under given significance level and establishing confidence interval of the shape parameter under the confidence coefficient.
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