The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications

  • Morad Alizadeh
  • Ahmed Z. Afify
  • M. S. EliwaEmail author
  • Sajid Ali
Original paper


In this paper, a new class of distributions called the odd log-logistic Lindley-G family is proposed. Several of its statistical and reliability properties are studied in-detail. One members of the proposed family can have symmetrical, right-skewed, leftt-skewed and reversed-J shaped densities, and decreasing, increasing, bathtub, unimodal and reversed-J shaped hazard rates. The model parameters are estimated using the maximum likelihood and Bayesian methods. Monte-Carlo simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. Finally, four real data sets are analyzed to show the flexibility of the new family.


Bayesian estimation Hazard rate function Lindley distribution Maximum likelihood Simulation 



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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsPersian Gulf UniversityBushehrIran
  2. 2.Department of Statistics, Mathematics and InsuranceBenha UniversityBenhaEgypt
  3. 3.Department of Mathematics, Faculty of ScienceMansoura UniversityMansouraEgypt
  4. 4.Department of StatisticsQuaid-i-Azam UniversityIslamabadPakistan

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