THE QUASI XGAMMA-POISSON DISTRIBUTION: PROPERTIES AND APPLICATION

Year 2018, Volume: 11 Issue: 3, 65 - 76, 31.12.2018

Subhradev Sen Mustafa Ç. Korkmaz , Haitham M. Yousof

Abstract

In this work, we introduce a new xgamma-Poisson lifetime model called the quasi xgamma-Poisson distribution. Some of its mathematical properties are derived. The proposed model can be motivated with a physical motivation by compounding the quasi xgamma construction with the truncated Poisson distribution. The quasi xgamma-Poisson model also motivated by the wide use of the xgamma distribution in many applied areas as well as for the fact that the new generalization provides more flexibility to analyze real data. We discuss the maximum likelihood estimation of the quasi xgamma-Poisson model parameters. An application to illustrate that the proposed quasi xgamma-Poisson model provides consistently better fit than the other competitive models.

Keywords

Xgamma-Poisson life distributions, zero-truncated poisson distribution, maximum likelihood estimation, order statistics

References

• Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108.
• Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N.(2008). A first course in order statistics, 54, Society of Industrial and Applied Mathematics.
• D.F. Andrews, D.F. and Herzberg, A. M. (1985). Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York.
• Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27(2), 154-161.
• Cooray, K., and Ananda, M. M. (2008). A generalization of the half-normal distribution with applications to lifetime data. Communications in Statistics–Theory and Methods, 37(9), 1323-1337.
• Evans, D. L., Drew, J. H. and Leemis, L. M. (2008). The distribution of the Kolmogorov-Smirnov, Cramervon Mises, and Anderson-Darling test statistics for exponential populations with estimated parameters. Communications in Statistics-Simulation and Computation, 37(7), 1396-1421.
• Gui, W., Zhang, S. and Lu, X. (2014). The Lindley-Poisson distribution in lifetime analysis and its properties. Hacettepe Journal of Mathematics and Statistics, 43(6), 1063-1077.
• Gupta, R. D. and Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
• Kus, C. (2007). A new lifetime distribution. Computational Statistics & Data Analysis, 51(9), 4497-4509.
• Lemonte, A. J. (2013). A new exponential-type distribution withconstant, decreasing, increasing, upsidedown bathtub and bathtub-shaped failure rate function. Computational Statistics & Data Analysis, 62, 149-170.
• Lu, W. and Shi, D. (2012). A new compounding life distribution: the Weibull-Poisson distribution. Journal of applied statistics, 39(1), 21-38.
• Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42(2), 299-302.
• Paraniaba, P. F., Ortega, E. M., Cordeiro, G. M. and Pascoa, M. A. D. (2013). The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 83(11), 2117-2143.
• Sen, S., Chandra, N. and Maiti, S. S. (2018). Survival estimation in xgamma distribution under progressively type-II right censored scheme. Model Assisted Statistics and Applications, 13(2), 107-121.
• Sen, S. and Chandra, N. (2017). The quasi xgamma distribution with application in bladder cancer data. Journal of Data Science, 15(1), 61-76.
• Sen, S., Maiti, S. S. and Chandra, N. (2016). The xgamma Distribution: Statistical properties and application. Journal of Modern Applied Statistical Method, 15(1), 774-788.
• Sen, S., Chandra, N. and Maiti, S. S. (2017). The weighted xgamma distribution: Properties and application. Journal of Reliability and Statistical Studies, 10(1), 43-58.
• Shaked, M. and Shanthikumar, J. G. (1994). Stochastic Orders and their Applications. Academic Press, New York.