Abstract
Using a progressive Type-I censoring technique, this article will explore how to estimate unknown parameters of the alpha power exponential distribution (APED) (Type-I PCS). The squared error loss function and the LINEX loss function are used to get the maximum likelihood estimate as well as the Bayesian estimation of the unknown parameters, respectively. It was our intention to use the Markov chain Monte Carlo method in conjunction with the Bayes estimation strategy. We are able to calculate the approximately accurate confidence intervals for the parameters whose values are unknown. In addition to this, we discussed the estimation challenges of reliability and the hazard rate function of the APED while using Type-I PCS, as well as the approximate confidence intervals that relate to these problems. In the last step, the theoretical findings that were acquired are evaluated and compared with the distributions of all of its rivals by making use of two actual datasets that represent the disciplines of engineering and medicine.