Journal of Data Science

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, R𝑒́nyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and intro-duced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.

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.