Simultaneous Inferences of Extreme Populations for Two-Parameter Exponential Populations Based on the Doubly Type II Censored Sample

[[abstract]]Some experimenters sometimes want to identify the worst and best Populations for the Two-Parameter Exponential Distributions at the same time for many biological or industrial experiments. Under the assumption of equal scale parameters, the best population is defined as the exponential population with the largest location parameter (UEP) and the worst population is defined as the exponential population with the smallest location parameter (LEP). In some lifetime test, the experimenter can only obtain incomplete sample, then the conventional inferential method for complete sample is no longer appropriate. Therefore, we proposed the simultaneous confidence intervals(SCI) for all distances from the worst and best populations (Extreme Populations) for Two-Parameter Exponential Distributions based on the Doubly Type-II censored sample. Without decreasing the probability of correct selection, the subset selection of extreme populations is also proposed. The critical values for Type-II doubly censored sample are tabulated. When and , the problem of simultaneous inferences of extreme populations reduced to the simultaneous inferences of the best populations. An numerical simulated example is given to illustrate all procedures.[[incitationindex]]E