Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution

This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.