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Stochastic dominance relations for generalised parametric distributions obtained through composition

Author

Listed:
  • Tommaso Lando

    (University of Bergamo
    VŠB-TU Ostrava)

  • Lucio Bertoli-Barsotti

    (University of Bergamo)

Abstract

Investigating stochastic dominance within flexible multi-parametric families of distributions is often complicated, owing to the high number of parameters or non-closed functional forms. To simplify the problem, we use the T–X method, making it possible to obtain generalised models through the composition of cumulative distributions and quantile functions. We derive conditions for the second-order stochastic dominance and for the increasing convex order within multi-parametric families in two steps, namely: (i) breaking them down via the T–X approach and (ii) checking dominance conditions of the (more) manageable distributions composing the model. We apply our method to some special distributions and focus on the beta-generated family, which enables the comparisons of order statistics of i.i.d. samples from (possibly) different random variables.

Suggested Citation

  • Tommaso Lando & Lucio Bertoli-Barsotti, 2020. "Stochastic dominance relations for generalised parametric distributions obtained through composition," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 297-311, December.
    • Handle: RePEc:spr:metron:v:78:y:2020:i:3:d:10.1007_s40300-020-00184-4
    DOI: 10.1007/s40300-020-00184-4
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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Belzunce, Félix & Martínez-Riquelme, Carolina & Ruiz, José M., 2013. "On sufficient conditions for mean residual life and related orders," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 199-210.
    3. Jorge Navarro & Yolanda del Águila & Miguel A. Sordo & Alfonso Suárez‐Llorens, 2013. "Stochastic ordering properties for systems with dependent identically distributed components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(3), pages 264-278, May.
    4. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    5. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    6. Wang, Shaun S. & Young, Virginia R., 1998. "Ordering risks: Expected utility theory versus Yaari's dual theory of risk," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 145-161, June.
    7. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    8. Sarabia, Jose Maria & Castillo, Enrique & Slottje, Daniel J., 2002. "Lorenz ordering between McDonald's generalized functions of the income size distribution," Economics Letters, Elsevier, vol. 75(2), pages 265-270, April.
    9. Kochar, Subhash, 2006. "Lorenz ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1855-1860, November.
    10. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    11. Ramos, Hector M. & Ollero, Jorge & Sordo, Miguel A., 2000. "A Sufficient Condition for Generalized Lorenz Order," Journal of Economic Theory, Elsevier, vol. 90(2), pages 286-292, February.
    12. M. H. Tahir & Gauss M. Cordeiro & Ayman Alzaatreh & M. Mansoor & M. Zubair, 2016. "The logistic-X family of distributions and its applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7326-7349, December.
    13. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
    14. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Second-order stochastic dominance for decomposable multiparametric families with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 159(C).
    15. Peter C. Fishburn, 1980. "Stochastic Dominance and Moments of Distributions," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 94-100, February.
    16. Wilfling, Bernd, 1996. "Lorenz ordering of generalized beta-II income distributions," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 381-388.
    17. Rachel J. Huang & Larry Y. Tzeng & Lin Zhao, 2020. "Fractional Degree Stochastic Dominance," Management Science, INFORMS, vol. 66(10), pages 4630-4647, October.
    18. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Distorted stochastic dominance: A generalized family of stochastic orders," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 132-139.
    19. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    20. Wilfling, Bernd, 1996. "Lorenz ordering of power-function order statistics," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 313-319, November.
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