Construction confidence interval for a linear combination of parameters of the two-parameter exponential distribution under type II progressive censoring

In this paper, to establish general and shortest confidence interval, for a linear combination of parameters of the two-parameter exponential distribution, we introduce a pivotal quantity. In the case of two populations, we use the method of variance estimate recovery and generalized pivotal quantities to construct a confidence interval for the difference of them. Based on the shortest confidence interval, we present a simple method to obtain its percentiles, and which a shorter confidence interval can be constructed. Also, the performances of the presented methods are studied by real data examples and simulations.

Keywords:

Percentiles , Modified based-normal asymptotic , Generalized pivotal quantity , Two-parameter exponential , Shortest confidence interval