The Odd Lindley Burr XII Model: Bayesian Analysis, Classical Inference and Characterizations

• Published in: Journal of Data Science Vol. 16; no. 2; pp. 327 - 353
• Main Authors: Korkmaz, Mustafa C¸a˘gatay, Yousof, Haitham M., Rasekhi, Mahdi, Hamedani, G. G.
• Format: Journal Article
• Language: English
• Published: 中華資料採礦協會 24.02.2021
• Subjects: Bayesian estimation; Simulation study; Multi- censored data; Burr XII model; Gibbs Algorithm; Markov Chain Monte Carlo; Metropolis-Hastings Algorithm
• ISSN: 1683-8602; 1680-743X; 1683-8602
• DOI: 10.6339/JDS.201804_16(2).0006

In this work, we study the odd Lindley Burr XII model initially introduced by Silva et al. [29]. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Some of its statistical structural properties including ordinary and incomplete moments, quantile and generating function and order statistics are derived. The odd Lindley Burr XII density can be expressed as a simple linear mixture of Burr XII densities. Useful characterizations are presented. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data. Bayesian estimation is performed by obtaining the posterior marginal distributions as well as using the simulation method of Markov Chain Monte Carlo (MCMC) by the Metropolis-Hastings algorithm in each step of Gibbs algorithm. The trace plots and estimated conditional posterior distributions are also presented.