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2020 | tom 26, nr 2 | 9--18
Tytuł artykułu

Excess Wealth Transform for Pareto Distributions

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper the notion of excess wealth transform and stochastic partial order based on it, introduced by Shaked and Shanthikumar (1998) are considered. The relations of the transform with the Lorenz curve and with certain variability measures are presented. The excess wealth transforms for Pareto type probability distributions are derived and their point-wise comparison is studied. (original abstract)
Rocznik
Numer
Strony
9--18
Opis fizyczny
Twórcy
  • University of Wrocław
Bibliografia
  • Arnold, B.C. (2008). Pareto and Generalized Pareto Distributions. In: D. Chotikapanich (ed.) Modeling Income Distributions and Lorenz Curves. Economic Studies in Equality, Social Exclusion and Well-Being, 5. New York, NY: Springer, 119-145. DOI:10.1007/978-0-387-72796-7_7.
  • Arnold, B.C. (2015). Pareto Distributions. Boca Raton, FL: CRC Press.
  • Belzunce, F., Martínez-Riquelme, C., Ruiz, J.M., Sordo, M.A. (2016). On sufficient conditions for the comparisons in the excess wealth order and spacings. Journal of Applied Probability, 53, 33-46. DOI:10.1017/jpr.2015.6.
  • Denuit, M., Vermandele, C. (1999). Lorenz and excess wealth orders, with applications in reinsurance theory. Scandinavian Actuarial Journal, 2,170-185. DOI:10.1080/03461239950132642.
  • Dhaene, J., Vanduffel, S., Goovaerts, M.J., Kaas, R., Tang, Q., Vyncke, D. (2006). Risk measures and comonotonicity: A review. Stochastic Models, 22, 573-606. DOI:10.1080/15326340600878016.
  • Fernández-Ponce, J.M., Pellerey, F., Rodríguez-Griñolo, M.R. (2011). A characterization of the multivariate excess wealth ordering. Insurance: Mathematics and Economics, 49, 410-417. DOI:10.1016/j.insmatheco.2011.07.001.
  • Fernández-Ponce, J.M., Kochar, S.C., Muñoz-Perez, J. (1998). Partial Orderings of Distributions Based on Right-Spread Functions. Journal of Applied Probability, 35(1), 221-228. DOI:10.1239/jap/1032192565.
  • Gastwirth, J. (1972). The Estimation of the Lorenz Curve and Gini Index. The Review of Economics and Statistics, 54 (3), 30-316. DOI:10.2307/1937992
  • Kayid, M., Al-Dokar, S. (2009). Some Results on the Excess Wealth Order with Applications in Reliability Theory. Contemporary Engineering Sciences, 2, 269-282.
  • Kochar, S., Li, X., Shaked, M. (2002). The total time on test transform and the excess wealth stochastic orders of distributions. Advances in Applied Probability, 34(4), 826-846.
  • Kochar, S., Xu, M. (2013). Excess Wealth Transform with Applications. In: H. Li, X. Li (eds.), Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics, 208, 273-288. New York, NY: Springer.
  • Markovich, N.M., Krieger, U.R. (2013). Analysis of Packet Transmission Processes in Peer-to-Peer Networks by Statistical Inference Methods. In: E. Biersack, C. Callegari, M. Matijasevic (eds.), Data Traffic Monitoring and Analysis. Lecture Notes in Computer Science, 7754, 104-119. Berlin: Springer. DOI:10.1007/978-3-642-36784-7_5.
  • Marshall, A.W., Olkin, I., Arnold, B.C. (2010). Stochastic Ordering. In: Inequalities: Theory of Majorization and Its Applications. Springer Series in Statistics, 693-756. New York, NY: Springer.
  • Muller, A., Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. Chichester: Wiley.
  • Pareto, V. (1897). Cours d'Economie Politique, 2. Lausanne.Shaked, M., Shanthikumar, J.G. (1998). Two probability orders. Probability in Engineering and Informational Sciences, 12, 1-23. DOI:10.1017/S0269964800005039.
  • Shaked, M., Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer.
  • Sordo, M.A. (2009). Comparing tail variabilities of risks by means of the excess wealth order. Insurance: Mathematics and Economics, 45, 466-469.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171605809

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