Hybrid Alpha Power Marshall Olkin G Class of Distributions

Fatimah Taher, Mohamed Bisher Zeina, Moustafa Mazhar Ranneh

Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria.

Emails: taherf597@gmail.com; bisher.zeina@gmail.com; moustafa.ranneh93@gmail.com

Abstract

This research presents a new class of probability distributions derived as a hybrid class between alpha power transformation class and Marshall Olkin G class and we call it the hybrid alpha power Marshall Olkin G class of distributions (HAPMOG). Characteristics properties of this new class were derived including moments, moments generating function, characteristic function, reliability and hazard functions, and its probability density function was presented in linear combination. Also, many generated distributions depending on this new class was presented and well-studied including HAPMOG-Exponential, HAPMOG-Weibull, HAPMOG-Freshet. This new class of distributions helps in modelling new forms of data, which has important applications in engineering, communication systems, networks modeling, etc.

Keywords: Probability Density Function; Cumulative Distribution Function; Alpha Power Transformation; Marshall Olkin G; Statistical Characteristics; Maximum Likelihood Estimation.