Odd Burr Power Lindley Distribution with Properties and Applications

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

1. 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.
2. Alizadeh, M., Mirmostafaei, S.M.T.K., Ghosh, I. Odd Log-logistic Power Lindley distribution, 2016, submitted.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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,.
8. Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31(4), 497-512.

9. 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.
10. Jorgensen, B., 1982, Statistical properties of the generalized inverse Gaussian distribution. New York: Springer-Verlag.