The exponentiated generalized power Lindley distribution: Properties and applications

  • S.M.T.K. MirMostafaeeEmail author
  • Morad Alizadeh
  • Emrah Altun
  • Saralees Nadarajah


In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived. Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions.


Anderson-Darling test statistic Exponentiated generalized class of distributions Lambert function Maximum likelihood method Power Lindley distribution 

MR Subject Classification

60E05 62F10 


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We would like to thank the referee for the valuable comments which led to this improved version of our manuscript.


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Copyright information

© Editorial Committee of Applied Mathematics 2019

Authors and Affiliations

  • S.M.T.K. MirMostafaee
    • 1
    Email author
  • Morad Alizadeh
    • 2
  • Emrah Altun
    • 3
  • Saralees Nadarajah
    • 4
  1. 1.Department of StatisticsUniversity of MazandaranBabolsarIran
  2. 2.Department of StatisticsPersian Gulf UniversityBushehrIran
  3. 3.Department of StatisticsBartin UniversityBartinTurkey
  4. 4.School of MathematicsUniversity of ManchesterManchesterUK

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