The Lindley family of distributions: properties and applications

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Cakmakyapan S., Ozel G.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.46, no.6, pp.1113-1137, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 6
  • Publication Date: 2017
  • Doi Number: 10.15672/hjms.201611615850
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1113-1137
  • Keywords: Lindley distribution, Lomax distribution, Weibull distribution, Estimation, Generating Function, Maximum Likelihood, Moments, Entropy, EXPONENTIATED WEIBULL FAMILY, GENERALIZED GAMMA-DISTRIBUTION
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we propose a new class of distributions called the Lindley generator with one extra parameter to generate many continuous distributions. The new distribution contains several distributions as sub-models, such as Lindley-Exponential, Lindley-Weibull, and Lindley-Lomax. Some mathematical properties of the new generator, including ordinary moments, quantile and generating functions, limiting behaviors, some entropy measures and order statistics, which hold for any baseline model, are presented. Then, we discuss the maximum likelihood method to estimate model parameters. The importance of the new generator is illustrated by means of three real data sets. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.