Title

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

Document Type

Article

Publication Date

4-2018

Publisher

Columbia University Department of Statistics

Source Publication

Journal of Data Science

Source ISSN

1680-743X

Original Item ID

10.6339/JDS.201804_16(2).0006

Abstract

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 BurrXII 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.

Comments

Journal of Data Science, Vol. 16, No. 2 (April 2018): 327-354. DOI.

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