Reliability Estimation for the Gull Alpha Power Pareto Model Under Progressive Type-I Censoring

A new family of Pareto distributions, known as the Gull Alpha Power Pareto (GAPP) model, has been derived and its statistical properties have been examined, followed by an application to life-testing, specifically under Type I progressive censoring schemes (PCS-TI). A comprehensive statistical analysis of the GAPP distribution was performed, including the estimation of its parameters and the reliability function. Estimation methods were investigated from an algorithmic perspective: for maximum likelihood estimation, the Newton-Raphson algorithm was adapted, while for Bayesian estimation, Markov Chain Monte Carlo methods were employed, utilizing the Metropolis-Hastings algorithm. Interval estimation was also addressed using two approaches: asymptotic confidence intervals based on MLE, and highest posterior density intervals in the Bayesian framework. A numerical study of the GAPP model under PCS-TI was performed using Monte Carlo simulations and real-world data related to the failure times of an airplane's air conditioning system. The results provided valuable insights into the performance of the estimation methods and algorithms, along with comparisons across different censoring schemes. To determine the optimal PCS-TI scheme, the study further examined the sampling optimality criteria under various patterns.