Statistical Inference for the Marshall-Olkin Extended Modified Inverse Rayleigh Distribution Under Adaptive Type-II Progressive Censoring

Hisham, K; Mokhlis, N A; Mansour, M

doi:10.21608/cjmss.2025.373673.1148

Statistical Inference for the Marshall-Olkin Extended Modified Inverse Rayleigh Distribution Under Adaptive Type-II Progressive Censoring

Document Type : Original Article

Authors

¹ Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt

² Department of Basic Science, Faculty of Engineering, The British University in Egypt, Cairo 11837, Egypt

10.21608/cjmss.2025.373673.1148

Abstract

The Marshall-Olkin extended modified inverse Rayleigh (MOEMIR) distribution, a new extension of the modified inverse Rayleigh} (MIR) distribution, is introduced as a member of a proposed \textit{Marshall-Olkin extended general inverse exponential (MOEGIE) family. This extension offers enhanced flexibility for modeling lifetime data. Statistical properties of the MOEGIE family are presented, and hence those of the MOEMIR distribution. Parameter estimation for the MOEMIR distribution is discussed under an adaptive Type-II progressive censoring scheme involving discrete uniformly distributed random removals. The parameters of the MOEMIR distribution are estimated using both maximum likelihood and Bayesian methods. The Bayesian estimation is refined under symmetric \textit{squared error loss} (SEL) and asymmetric \textit{linear exponential loss} (LINEX) functions, using a \textit{Metropolis-Hastings} (M-H) sampling method of the \textit{Markov chain Monte Carlo} (MCMC) technique. A simulation study is performed to highlight the obtained theoretical results. Finally, the utility of the MOEMIR distribution is demonstrated using a real-world dataset involving the remission times of patients with bladder cancer.

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