The complementary odd Weibull power series distribution: properties and applications

Document Type : Original Article


Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran


In this paper, a new four-parameters model called the complementary odd Weibull power series (COWPS) distribution is defined and its properties are explored. This new distribution exhibits several new and well-known hazard rate shapes such as increasing, decreasing, bathtub-shaped and J-shape hazard rates. Some of its mathematical properties are obtained including moments, quantiles reliability, and moment generating functions. The maximum likelihood estimation method is used to estimate the vector of parameters. A simulation study is presented to investigate the performance of the estimators. Finally, The usefulness of the model has been demonstrated by applying it to a real-life dataset.


Main Subjects

[1] M. Alizadeh, M. Emadi, M. Doostparast, G. M. Cordeiro, E. Ortega, R. Pescim, A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications, Hacet. J. Math. Stat. 44(6) (2015) 1491-1512.
[2] M. Alizadeh, H. M. Yousof, M. Rasekhi, E. Altun, The odd Log-Logistic Poisson-G family of distributions, J. Math. Exten., 12(3) (2018) 81-104.
[3] W. Barreto-Souza, A. H. S. Santos, G. M. Cordeiro, The beta generalized exponential distribution, J. Stat. Comput. Simul. 80(1-2) (2010) 159-172.
[4] V. G. Canchoa, F. Louzada-Neto, G. D.C. Barriga, The Poisson-exponential lifetime distribution, Computational Statistics and Data Analysis, 55 (2011) 677-686.
[5] K. Cooray, Generalization of the Weibull distribution: the odd Weibull family, Statistical Modelling, 6 (2006) 265-277.
[6] G. M. Cordeiro, M. Alizadeh, E. M. M. Ortega, L. H. Valdivieso Serrano, The Zografos-Balakrishnan odd log-logistic family of distributions: properties and applications, Hacet. J. Math. Stat, 45(6) (2016) 1781-1803.
[7] G. M. Cordeiro, M. Alizadeh, M. H. Tahir, M. Mansoor, M. Bourguignon, G. G. Hamedani, The beta odd log-logistic generalized family of distributions, Hacet. J. Math. Stat, 45 (2016) 1175-1202.
[8] G. M. Cordeiro, R. B. Silva, The complementary extended Weibull power series class of distributions, Ciˆencia e Natura, 36 (2014) 1-13.
[9] D. Cox, D. Hinkley, Theoretical Statistics, Chapman and Hall, New York, first edition, 1979.
[10] I. Elbatal, A. Asgharzadeh, F. Sharafi, A new class of generalized power Lindley distributions, Journal of Applied Probability and Statistics, 10 (2015) 89-116.
[11] F. Famoye, C. Lee, O. Olumolade, The beta-Weibull distribution, J. Stat. Theory Appl., 4(2) (2005) 121-136.
[12] J. Flores, P. Borges, V. G. Cancho, F. Louzada, The complementary exponential power series distribution, Brazilian Journal of Probability and Statistics, 27 (2013) 565-584.
[13] M. Goldoust, S. Rezaei, Y. Si, S. Nadarajah, Lifetime distributions motivated by series and parallel structures, Comm. Statist. Simulation Comput. 48(2) (2019) 556-579.
[14] A. W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84(3) (1997) 641-652.
[15] B. G. Munteanu, A. Leahu, I. Pˆartachi, The max-Weibull power series distribution, An. Univ. Oradea Fasc. Mat., 21(2) (2014) 133-139.
[16] A. Noack, A class of random variables with discrete distributions, Ann. Math. Statistics, 21 (1950) 127-132.