The Slash Lindley-Weibull Distribution

  • Jimmy Reyes
  • Yuri A. Iriarte
  • Pedro Jodrá
  • Héctor W. GómezEmail author


In this paper, a new class of slash distribution is introduced. The distribution is obtained as a quotient of two independent random variables, specifically, a Lindley-Weibull distribution divided by a power of a uniform distribution. The new model can be considered as an extension of the Lindley-Weibull law more flexible in terms of the kurtosis of the distribution. Some statistical properties are studied and the parameter estimation problem is carried out by the maximum likelihood method. The performance of this method is assessed via a Monte Carlo simulation study. A real data application illustrates the usefulness of the proposed distribution to model data with excess kurtosis.


Lindley-Weibull distribution Kurtosis Maximum likelihood 

Mathematics Subject Classification (2010)

60E05 62F10 


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The research of J. Reyes and H.W. Gómez has been partially funded by grant SEMILLERO UA-2016.


  1. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bhati D, Malik MA, Vaman HJ (2015) Lindley-exponential distribution: properties and applications. Metron 73:335–357MathSciNetCrossRefzbMATHGoogle Scholar
  3. Cakmakyapan S, Ozel G (2015) The Lindley family of distributions: Properties and applications, Hacettepe Journal of Mathematics and Statistics.
  4. Development Core Team (2016) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. Google Scholar
  5. Ghitany ME, Atieh B, Nadarajah S (2008) Lindley distribution and its application. Math Comput Simul 78:493–506MathSciNetCrossRefzbMATHGoogle Scholar
  6. Gómez HW, Venegas O (2008) Erratum to: A new family of slash-distributions with elliptical contours. Statist Probab Lett 77(2007):717–725. Stat. Probab. Lett. 78, 2273–2274zbMATHGoogle Scholar
  7. Gómez HW, Quintana FA, Torres FJ (2007) A new family of slash-distributions with elliptical contours. Stat Probab Lett 77:717–725MathSciNetCrossRefzbMATHGoogle Scholar
  8. Gómez HW, Olivares-Pacheco JF, Bolfarine H (2009) An extension of the generalized Birnbaum–Saunders distribution. Stat Probab Lett 79:331–338MathSciNetCrossRefzbMATHGoogle Scholar
  9. Gui W (2014) Statistical properties and applications of the slash Lindley distribution. J Appl Stat Sci 20:283–298zbMATHGoogle Scholar
  10. Iriarte YA, Gómez HW, Varela H, Bolfarine H (2015) Slashed Rayleigh distribution. Rev Colomb Estadí,stica 38:31–44MathSciNetCrossRefzbMATHGoogle Scholar
  11. Jodrá P (2010) Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function. Math Comput Simul 81:851–859MathSciNetCrossRefzbMATHGoogle Scholar
  12. Lindley DV (1958) Fiducial distributions and Bayes’ theorem. J Roy Statist Soc Ser B 20:102–107MathSciNetzbMATHGoogle Scholar
  13. Marshall A, Olkin I (1997) A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84:641–652MathSciNetCrossRefzbMATHGoogle Scholar
  14. Olivares J, Cornide H, Monasterio M (2010) An extension of the two-parameter Weibull distribution. Rev Colomb Estadí,stica 33:219–231MathSciNetGoogle Scholar
  15. Olmos NM, Varela H, Gómez HW, Bolfarine H (2012) An extension of the half-normal distribution. Stat Papers 53:875–886MathSciNetCrossRefzbMATHGoogle Scholar
  16. Olmos NM, Varela H, Bolfarine H, Gómez HW (2014) An extension of the generalized half-normal distribution. Stat Papers 55:967–981MathSciNetCrossRefzbMATHGoogle Scholar
  17. Paris RB (2010) Incomplete gamma and related functions. In: Olver FWF, Lozier DW, Boisvert RF, Clark CW (eds) NIST Handbook of mathematical functions, national institute of standards and technology. Cambridge University Press, Cambridge, pp 173–192Google Scholar
  18. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464MathSciNetCrossRefzbMATHGoogle Scholar
  19. Shaw W, Buckley I (2007) The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. IMA, Primera Conferencia sobre Finanzas Computacionales, Cornell University, arXiv:0901.0434
  20. Zografos K, Balakrishnan N (2009) On families of beta- and generalized gamma-generated distributions and associated inference. Stat Methodol 6:344–362MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jimmy Reyes
    • 1
  • Yuri A. Iriarte
    • 1
  • Pedro Jodrá
    • 2
  • Héctor W. Gómez
    • 1
    Email author
  1. 1.Departamento de Matemáticas, Facultad de Ciencias BásicasUniversidad de AntofagastaAntofagastaChile
  2. 2.Departamento de Métodos EstadísticosUniversidad de ZaragozaZaragozaSpain

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