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Year 2023, Volume: 52 Issue: 2, 529 - 545, 31.03.2023
https://doi.org/10.15672/hujms.820849

Abstract

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.

Comparing discrete Pareto populations under a fixed effects model

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

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.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Mohammad Baratnia This is me 0000-0003-2089-6652

Abdolhamid Rezaei Roknabady 0000-0002-3420-9027

Mahdi Doostparast 0000-0002-4614-8137

Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 52 Issue: 2

Cite

APA Baratnia, M., Rezaei Roknabady, A., & Doostparast, M. (2023). Comparing discrete Pareto populations under a fixed effects model. Hacettepe Journal of Mathematics and Statistics, 52(2), 529-545. https://doi.org/10.15672/hujms.820849
AMA Baratnia M, Rezaei Roknabady A, Doostparast M. Comparing discrete Pareto populations under a fixed effects model. Hacettepe Journal of Mathematics and Statistics. March 2023;52(2):529-545. doi:10.15672/hujms.820849
Chicago Baratnia, Mohammad, Abdolhamid Rezaei Roknabady, and Mahdi Doostparast. “Comparing Discrete Pareto Populations under a Fixed Effects Model”. Hacettepe Journal of Mathematics and Statistics 52, no. 2 (March 2023): 529-45. https://doi.org/10.15672/hujms.820849.
EndNote Baratnia M, Rezaei Roknabady A, Doostparast M (March 1, 2023) Comparing discrete Pareto populations under a fixed effects model. Hacettepe Journal of Mathematics and Statistics 52 2 529–545.
IEEE M. Baratnia, A. Rezaei Roknabady, and M. Doostparast, “Comparing discrete Pareto populations under a fixed effects model”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, pp. 529–545, 2023, doi: 10.15672/hujms.820849.
ISNAD Baratnia, Mohammad et al. “Comparing Discrete Pareto Populations under a Fixed Effects Model”. Hacettepe Journal of Mathematics and Statistics 52/2 (March 2023), 529-545. https://doi.org/10.15672/hujms.820849.
JAMA Baratnia M, Rezaei Roknabady A, Doostparast M. Comparing discrete Pareto populations under a fixed effects model. Hacettepe Journal of Mathematics and Statistics. 2023;52:529–545.
MLA Baratnia, Mohammad et al. “Comparing Discrete Pareto Populations under a Fixed Effects Model”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, 2023, pp. 529-45, doi:10.15672/hujms.820849.
Vancouver Baratnia M, Rezaei Roknabady A, Doostparast M. Comparing discrete Pareto populations under a fixed effects model. Hacettepe Journal of Mathematics and Statistics. 2023;52(2):529-45.