Properties and Application of Alpha Power Transformed Perks Distribution to Engineering Data - Yakura, Bassa Shiwaye; Aniah-Betiang, Elizabeth Ishagba; Koleoso, Peter O.; Ieren, Terna Godfrey (Mikailalsys Journal of Mathematics and Statistics, 2026)
This study introduces the Alpha Power Transformed Perks Distribution (APTPD), obtained by applying the alpha power transformation method to the classical Perks distribution in order to enhance its flexibility and enable it to accommodate different data structures. Several analytical properties of the proposed distribution are established, including a simplified expression for its probability density function, ordinary moments, moment-generating and characteristic functions, reliability measures, and order statistics. The parameter estimation for the APTPD is conducted using the method of maximum likelihood. To demonstrate its practical relevance, the APTPD is fitted to an engineering dataset on aircraft windshield service times and compared with several existing generalizations of the Perks distribution. Based on multiple goodness-of-fit statistics and information criteria, the APTPD provides the best fit among the considered competing models. Overall, the results indicate that the proposed distribution is a useful and flexible model for analyzing positively skewed lifetime data in reliability and survival studies.