The Marshall-Olkin Odd Lindley-G Family of Distributions: Theory and Applications

Abstract

In this paper, we propose a new family of distributions called the Marshall-Olkin odd Lindley-G family of distributions. It is constructed from the Marshall-Olkin transformation and the odd Lindley-G family of distributions introduced by Gomes-Silva et al. [10]. We study the fundamental mathematical properties of this new family and highlight its ability to provide appropriate statistical models for various kinds of data. A particular attention is paid on a special model with four parameters, using the Burr III distribution as baseline. We then estimate the model parameters  by the maximum likelihood method. A simulation study is performed to check the asymptotic behavior of the maximum likelihood estimates. Four applications with practical data sets are considered to see the usefulness of the proposed family.