Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data
We develop an exact inference for the location and the scale parameters of the two-exponential distribution and the Pareto distribution based on their maximum-likelihood estimators from the doubly Type-II and the progressive Type-II censored sample. Based on some pivotal quantities,
exact confidence intervals and tests of hypotheses are constructed. Exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of
these pivotal quantities. We also provide a bootstrap method for constructing a confidence interval. Some simulation studies are carried out to assess their performances. Using the exact distribution of the scale parameter, we establish an acceptance sampling procedure based on the lifetime
of the unit. Some numerical results are tabulated for the illustration. One biometrical example is also given to illustrate the proposed methods.
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acceptance sampling plan;
two-parameter exponential distribution
Document Type: Research Article
School of Mathematics and Computation Science, Zhanjiang Normal University, Zhanjiang, Guangdong, 524048, People's Republic of China
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People's Republic of China
School of Management, Lanzhou University, Lanzhou, Gansu, 730000, People's Republic of China
July 1, 2013