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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

Abstract

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.

Keywords

Bayesian estimation Hazard rate function Lindley distribution Maximum likelihood Simulation 

Notes

References

  1. Afify AZ, Cordeiro GM, Mead ME, Alizadeh M, Al-Mofleh H, Nofal ZM (2019) The generalized odd Lindley-G family: properties and applications. Anais da Academia Brasileira de Ciências 91:1–22CrossRefGoogle Scholar
  2. Afify AZ, Cordeiro GM, Yousof HM, Alzaatreh A, Nofal ZM (2016) The Kumaraswamy transmuted-G family of distributions: properties and applications. J Data Sci 14:245–270Google Scholar
  3. Afify AZ, Cordeiro GM, Yousof HM, Saboor A, Ortega EMM (2018) The Marshall–Olkin additive Weibull distribution with variable shapes for the hazard rate. Hacettepe J Math Stat 47:365–381MathSciNetzbMATHGoogle Scholar
  4. Alizadeh M, Emadi M, Doostparast M, Cordeiro GM, Ortega EMM, Pescim RR (2015) A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepe J Math Stat 44:1491–1512MathSciNetzbMATHGoogle Scholar
  5. Alizadeh M, Lak F, Rasekhi M, Ramires TG, Yousof HM, Altun E (2018) The odd log-logistic Topp-Leone G family of distributions: heteroscedastic regression models and applications. Comput Stat 33:1217–1244MathSciNetCrossRefGoogle Scholar
  6. Altun G, Alizadeh M, Altun E, Özel G (2017) Odd Burr Lindley distribution with properties and applications. Hacettepe J Math Stat 46:255–276MathSciNetzbMATHGoogle Scholar
  7. Alzaatreh A, Lee C, Famoye F (2013) A new method for generating families of continuous distributions. Metron 71:63–79MathSciNetCrossRefGoogle Scholar
  8. Bakouch HS, Al-Zahrani BM, Al-Shomrani AA, Marchi VA, Louzada F (2012) An extended Lindley distribution. J Korean Stat Soc 41:75–85MathSciNetCrossRefGoogle Scholar
  9. Barreto-Souza W, Santos AH, Cordeiro GM (2010) The beta generalized exponential distribution. J Stat Comput Simul 80:159–172MathSciNetCrossRefGoogle Scholar
  10. Chang GJ, Cui L, Hwang FK (2009) Reliabilities of consecutive k-out- of-n: F systems. J Stat Theory Appl 7:435–452Google Scholar
  11. Cordeiro GM, Afify AZ, Ortega EMM, Suzuki AK, Mead ME (2019) The odd Lomax generator of distributions: properties, estimation and applications. J Comput Appl Math 347:222–237MathSciNetCrossRefGoogle Scholar
  12. Cordeiro GM, Alizadeh M, Ortega EMM, Serrano LHV (2016a) The Zografos-Balakrishnan odd log-logistic family of distributions: properties and applications. Hacettepe J Math Stat 45:1781–1803MathSciNetzbMATHGoogle Scholar
  13. Cordeiro GM, Alizadeh M, Tahir MH, Mansoor M, Bourguignon M, Hamedani GG (2016b) The beta odd log-logistic generalized family of distributions. Hacettepe J Math Stat 45:1175–1202MathSciNetzbMATHGoogle Scholar
  14. El-Morshedy M, Eliwa MS, Nagy H (2019) A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications. J Appl Stat.  https://doi.org/10.1080/02664763.2019.1638893 CrossRefGoogle Scholar
  15. El-Morshedy M, Eliwa MS (2019) The odd flexible Weibull-H family of distributions: properties and estimation with applications to complete and upper record data. Filomat, To appearGoogle Scholar
  16. Eliwa MS, El-Morshedy M, Ibrahim M (2018) Inverse Gompertz distribution: properties and different estimation methods with application to complete and censored data. Ann Data Sci.  https://doi.org/10.1007/s40745-018-0173-0 CrossRefGoogle Scholar
  17. Eliwa, M. S., El-Morshedy, M. and Afify, A. Z. (2019). The odd Chen generator of distributions: properties and estimation methods with applications in medicine and engineering. Journal of the National Science Foundation of Sri Lanka. To appearGoogle Scholar
  18. Ghitany ME, Al-Mutairi DK, Balakrishhnan N, Al-Enezi LJ (2013) Power Lindley distribution and associated inference. Comput Stat Data Anal 64:20–33MathSciNetCrossRefGoogle Scholar
  19. Ghitany ME, Alqallaf F, Al-Mutairi DK, Husain HA (2011) A two-parameter weighted Lindley distribution and its applications to survival data. Math Comput Simul 81:1190–1201MathSciNetCrossRefGoogle Scholar
  20. Gleaton JU, Lynch JD (2006) Properties of generalized log-logistic families of lifetime distributions. J Prob Stat Sci 4:51–64MathSciNetGoogle Scholar
  21. Gomes-Silva F, Percontin A, Brito E, Ramos MW, Venâncio R, Cordeiro GM (2017) The odd Lindley-G family of distributions. Austrian J Stat.  https://doi.org/10.17713/ajs.v46i1.222 CrossRefGoogle Scholar
  22. Gupta RD, Kundu D (2001) Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biometrical J J Math Methods Biosci 43:117–130MathSciNetzbMATHGoogle Scholar
  23. Hassan AS, Nassr SG (2018) Power Lindley-G family of distributions. Ann Data Sci.  https://doi.org/10.1007/s40745-018-01 CrossRefGoogle Scholar
  24. Jehhan A, Mohamed I, Eliwa MS, Al-mualim S, Yousof HM (2018) The two-parameter odd Lindley Weibull lifetime model with properties and applications. Int J Stat Prob 7:57–68CrossRefGoogle Scholar
  25. Jodrá P (2010) Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function. Math Comput Simul 81:851–859MathSciNetCrossRefGoogle Scholar
  26. Khan MS, King R, Hudson I (2017) Transmuted generalized exponential distribution: a generalization of the exponential distribution with applications to survival data. Commun Stat Simul Comput 46:4377–98MathSciNetCrossRefGoogle Scholar
  27. Mahdavi A, Kundu D (2016) A new method for generating distributions with an application to exponential distribution. Commun Stat Theory Methods 46:6543–6557MathSciNetCrossRefGoogle Scholar
  28. Mahmoudi E, Zakerzadeh H (2010) Generalized Poisson-Lindley distribution. Commun Stat Theory Methods 39:1785–1798MathSciNetCrossRefGoogle Scholar
  29. Merovci F (2013) Transmuted Lindley distribution. Int J Open Prob Comput Sci Math 6:63–72CrossRefGoogle Scholar
  30. Mudholkar GS, Srivastava DK, Kollia GD (1996) A generalization of the Weibull distribution with application to the analysis of survival data. J Am Stat Assoc 91:1575–1583MathSciNetCrossRefGoogle Scholar
  31. Murthy DP, Xie M, Jiang R (2004) Weibull models. Wiley, HobokenzbMATHGoogle Scholar
  32. Nadarajah S, Kotz S (2006) The beta exponential distribution. Reliab Eng Syst Saf 91:689–697CrossRefGoogle Scholar
  33. Nadarajah S, Bakouch HS, Tahmasbi R (2011) A generalized Lindley distribution. Sankhya B 73:331–359MathSciNetCrossRefGoogle Scholar
  34. Nassar M, Afify AZ, Dey S, Kumar D (2018) A new extension of Weibull distribution: properties and different methods of estimation. J Comput Appl Math 336:439–457MathSciNetCrossRefGoogle Scholar
  35. Nichols MD, Padgett WJ (2006) A bootstrap control chart for Weibull percentiles. Qual Reliab Eng Int 22:141–151CrossRefGoogle Scholar
  36. Nofal ZM, Afify AZ, Yousof HM, Cordeiro GM (2017) The generalized transmuted-G family of distributions. Commun Stat Theory Methods 46:4119–4136MathSciNetCrossRefGoogle Scholar
  37. Özel G, Alizadeh M, Cakmakyapan S, Hamedani G, Ortega EMM, Cancho G (2017) The odd log-logistic Lindley Poisson model for lifetime data. Commun Stat Simul Comput 46:6513–6537MathSciNetCrossRefGoogle Scholar
  38. Pararai M, Warahena-Liyanage G, Oluyede BO (2015) A new class of generalized power Lindley distribution with applications to lifetime data. Theor Math Appl 5:53–96zbMATHGoogle Scholar
  39. Shanker R, Sharma S, Shanker R (2013) A two-parameter Lindley distribution for modeling waiting and survival times data. Appl Math 4:363–368CrossRefGoogle Scholar
  40. Sharma V, Singh S, Singh U, Agiwal V (2015) The inverse Lindley distribution: a stress-strength reliability model with applications to head and neck cancer data. J Ind Prod Eng 32:162–173Google Scholar
  41. Smith RL, Naylor JC (1987) A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. J Appl Stat 36:358–369MathSciNetCrossRefGoogle Scholar
  42. Zeghdoudi H, Nedjar S (2016) Gamma Lindley distribution and its application. J Appl Prob Stat 11:129–138zbMATHGoogle Scholar
  43. Zeghdoudi H, Nedjar S (2017) On Poisson pseudo Lindley distribution: properties and applications. J Prob Stat Sci 15:19–28Google Scholar

Copyright information

© 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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