Comparing discrete Pareto populations under a fixed effects model

Year 2023, Volume: 52 Issue: 2, 529 - 545, 31.03.2023

Mohammad Baratnia Abdolhamid Rezaei Roknabady , Mahdi Doostparast

https://doi.org/10.15672/hujms.820849

Abstract

The discrete Pareto distribution can be considered as a lifetime distribution and then is widely used in practice. It follows the power law tails property which makes it as a candidate model for natural phenomena. This paper deals with comparison of discrete Pareto populations by proposing a non-linear fixed effects model. Estimators for the factor effects are derived in explicit expressions. Stochastic properties of the estimators are studied in details. A test for assessing the homogeneity of populations is proposed. Illustrative examples are also given. The proposed model is an alternative model for analyzing data sets in which the linear models have poor performance.

Keywords

Non-linear models , one-way classification , fixed effects , estimation , discrete Pareto population

References

• [1] M. Baratnia and M. Doostparast, One-way classification with random effects: A reversed-hazard-based approach, J. Comput. Appl. Math. 349, 60–69, 2019.
• [2] M. Baratnia and M. Doostparast, A random effects model for comparing pareto populations, Comput Ind Eng 147, 106612, 2020.
• [3] A. Buddana and T.J. Kozubowski, Discrete pareto distributions, Stoch. Qual 29, 143–156, 2014.
• [4] G. Casella and R.L. Berger, Statistical Inference, 2nd Edition, Thomson Learning, 2002.
• [5] S.R. Cole, H. Chu and S. Greenland, Maximum likelihood, profile likelihood, and penalized likelihood: A primer, Am. J. Epidemiol. 179, 252–260, 2014.
• [6] A. Gut, Probability: A Graduate Course, 2nd Edition, Springer, 2013.
• [7] J. Jiang, Linear and Generalized Linear Mixed Models and Their Applications, Springer, 2007.
• [8] A.I. Khuri, Advanced Calculus with Applications in Statistics: 2nd Edition Revised and Expanded, Wiley, 2003.
• [9] T.J. Kozubowski, A.K. Panorska and M.L. Forister, A discrete truncated pareto distribution, Stat. Methodol. 26, 135–150, 2015.
• [10] H. Krishna and P.S. Pundir, Discrete burr and discrete pareto distributions, Stat. Methodol. 6, 177–188, 2009.
• [11] W.H. Kruskal and W.A. Wallis, Use of ranks in one-criterion variance analysis, J Am Stat Assoc 47, 583–621, 1952.
• [12] E.L. Lehmann and G. Casella, Theory of Point Estimation, 2nd Edition, Springer, 1998.
• [13] J.T. McClave and F.H. Dietrich, Statistics, Dellen Publishing, 1991.
• [14] C.E. McCulloch, S.R. Searle and J.M. Neuhaus, Generalized, Linear, and Mixed Models, 2nd Edition, Wiley, 2008.
• [15] J.A. Nelder and R.W.M. Wedderburn, Generalized linear models, J R Stat Soc Ser A Stat Soc 135, 370–384, 1972.
• [16] S.R. Searle, G. Casella and C.E. McCulloch, Variance Components, Wiley, 1992.