Optimal parameter estimation of the two-parameter bathtub-shaped lifetime distribution based on a type II right censored sample

This paper proposes different types of exact (or approximate) confidence intervals and exact (or approximate) joint confidence regions for the parameters of the two-parameter lifetime distribution with bathtub-shaped or increasing failure rate (IFR) function based on a type II right censored sample. Moreover, we provide optimal criteria for finding a best exact (or approximate) confidence interval and a best exact (or approximate) joint confidence region among these estimations. Two examples are used to compare our proposed method to the existing approach of [Statistics & Probability Letters 49 (2000) 155].