Research Article
BibTex RIS Cite

Odd Burr Power Lindley Distribution with Properties and Applications

Year 2017, Volume: 30 Issue: 3, 139 - 159, 20.09.2017

Emrah Altun Morad Alizadeh Gamze Ozel

Abstract

We introduce a four-parameter distribution, called odd
Burr power Lindley distribution, which extends the Lindley distribution and has
increasing, upside-down and bathtub shapes for the hazard rate function. Our
purpose is to provide a generalization that may be useful to still more complex
situations. It includes as special sub-models some well-known distributions
such as Lindley, power Lindley, odd log-logistic Lindley, among others. Several
statistical properties of the distribution are explored. A simulation study is
performed to assess the maximum likelihood estimations of introduced
distribution parameters in terms of bias and mean square error, estimated
average length and coverage probability.

Keywords

maximum likelihood estimation simulation quantile function moment

References

  • Alizadeh, M., Cordeiro, G. M., Nascimento, A.D.C., M.C.S., Lima, Ortega, E.M.M, Odd-Burr generalized family of distributions with some applications, 2016, Journal of Statistical Computation and Simulation, DOI:10.1080/00949655.2016.1209200.
  • Alizadeh, M., Mirmostafaei, S.M.T.K., Ghosh, I. Odd Log-logistic Power Lindley distribution, 2016, submitted.
  • Andrews, D. F., Herzberg, A. M., 1985, Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York.
  • Cakmakyapan, S., Ozel, G., 2014, A new customer lifetime duration distribution: The Kumaraswamy Lindley distribution, International Journal of Trade, Economics and Finance, 5 (5), 441-444.
  • Cordeiro, G. M., Alizadeh, M., Tahir, M. H., Mansoor, M., Bourguignon, M., Hamedani, G. G., 2015, The Beta Odd Log-Logistic Generalized Family of Distributions, Hacettepe Journal of Mathematics and Statistics, 45, 73, DOI: 10.15672/HJMS.20157311545.
  • Cordeiro, G. M., Ortega, E. M., & da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1), 1-27.
  • Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., Knuth, D. E., 1996, On the Lambert W Function, Adv. Comput. Math. 5, 329-359,.
  • Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31(4), 497-512.
  • Ghitany, M.E., Al-Mutairi, D.K., Balakrishnan, N., Al-Enezi, L.J., 2013, Power Lindley distribution and associated inference, Computational Statistics and Data Analysis, 64, 20-33.
  • Jorgensen, B., 1982, Statistical properties of the generalized inverse Gaussian distribution. New York: Springer-Verlag.

Year 2017, Volume: 30 Issue: 3, 139 - 159, 20.09.2017

Emrah Altun Morad Alizadeh Gamze Ozel

Abstract

References

  • Alizadeh, M., Cordeiro, G. M., Nascimento, A.D.C., M.C.S., Lima, Ortega, E.M.M, Odd-Burr generalized family of distributions with some applications, 2016, Journal of Statistical Computation and Simulation, DOI:10.1080/00949655.2016.1209200.
  • Alizadeh, M., Mirmostafaei, S.M.T.K., Ghosh, I. Odd Log-logistic Power Lindley distribution, 2016, submitted.
  • Andrews, D. F., Herzberg, A. M., 1985, Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York.
  • Cakmakyapan, S., Ozel, G., 2014, A new customer lifetime duration distribution: The Kumaraswamy Lindley distribution, International Journal of Trade, Economics and Finance, 5 (5), 441-444.
  • Cordeiro, G. M., Alizadeh, M., Tahir, M. H., Mansoor, M., Bourguignon, M., Hamedani, G. G., 2015, The Beta Odd Log-Logistic Generalized Family of Distributions, Hacettepe Journal of Mathematics and Statistics, 45, 73, DOI: 10.15672/HJMS.20157311545.
  • Cordeiro, G. M., Ortega, E. M., & da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1), 1-27.
  • Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., Knuth, D. E., 1996, On the Lambert W Function, Adv. Comput. Math. 5, 329-359,.
  • Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31(4), 497-512.
  • Ghitany, M.E., Al-Mutairi, D.K., Balakrishnan, N., Al-Enezi, L.J., 2013, Power Lindley distribution and associated inference, Computational Statistics and Data Analysis, 64, 20-33.
  • Jorgensen, B., 1982, Statistical properties of the generalized inverse Gaussian distribution. New York: Springer-Verlag.
There are 10 citations in total.

Details

Journal Section Statistics
Authors

Emrah Altun

Morad Alizadeh

Gamze Ozel

Publication Date September 20, 2017
Published in Issue Year 2017 Volume: 30 Issue: 3

Cite

APA Altun, E., Alizadeh, M., & Ozel, G. (2017). Odd Burr Power Lindley Distribution with Properties and Applications. Gazi University Journal of Science, 30(3), 139-159.
AMA Altun E, Alizadeh M, Ozel G. Odd Burr Power Lindley Distribution with Properties and Applications. Gazi University Journal of Science. September 2017;30(3):139-159.
Chicago Altun, Emrah, Morad Alizadeh, and Gamze Ozel. “Odd Burr Power Lindley Distribution With Properties and Applications”. Gazi University Journal of Science 30, no. 3 (September 2017): 139-59.
EndNote Altun E, Alizadeh M, Ozel G (September 1, 2017) Odd Burr Power Lindley Distribution with Properties and Applications. Gazi University Journal of Science 30 3 139–159.
IEEE E. Altun, M. Alizadeh, and G. Ozel, “Odd Burr Power Lindley Distribution with Properties and Applications”, Gazi University Journal of Science, vol. 30, no. 3, pp. 139–159, 2017.
ISNAD Altun, Emrah et al. “Odd Burr Power Lindley Distribution With Properties and Applications”. Gazi University Journal of Science 30/3 (September 2017), 139-159.
JAMA Altun E, Alizadeh M, Ozel G. Odd Burr Power Lindley Distribution with Properties and Applications. Gazi University Journal of Science. 2017;30:139–159.
MLA Altun, Emrah et al. “Odd Burr Power Lindley Distribution With Properties and Applications”. Gazi University Journal of Science, vol. 30, no. 3, 2017, pp. 139-5.
Vancouver Altun E, Alizadeh M, Ozel G. Odd Burr Power Lindley Distribution with Properties and Applications. Gazi University Journal of Science. 2017;30(3):139-5.