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.
Highlights
Resembling the Pearson system of distributions [9, 10], Burr [5] presented a system that incorporates twelve types of cdfs which yield an assortment of density shapes
The goal of this article is to study the Odd Lindley-BXII (OLBXII) model first introduced by Silva et al [29] using the odd Lindley-G (OL-G) family of distributions
Let X1, ⋯,Xn be a random sample of size n from the OLBXII distribution and let X1:n, X2:n, ⋯,Xn:n be the corresponding order statistics.the pdf of the ith order statistic Xi:n, say fi:n(x),is given by fi:n(x)
Summary
Resembling the Pearson system of distributions [9, 10], Burr [5] presented a system that incorporates twelve types of cdfs (cumulative distribution function) which yield an assortment of density shapes. Burr [5, 6], Hatke [16], Burr and Cislak [7] and Rodriguez [26] paid special attention to one of these forms, Type XII, whose distribution function G(x) is given by Both α and β are positive shape parameters. The cdf and the reliability function of the Burr-XII (BXII) model can be written in a closed form. Silva et al [30] proposed a new location–scale regression model based on BXII model and introduced the log-Burr XII regression models with censored data. The goal of this article is to study the Odd Lindley-BXII (OLBXII) model first introduced by Silva et al [29] using the odd Lindley-G (OL-G) family of distributions.
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