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Excess Wealth Transform with Applications

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Stochastic Orders in Reliability and Risk

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 208))

Abstract

Shaked and Shanthikumar [425] introduced the excess wealth transform and the related excess wealth order. A lot of research activities have taken place on this topic lately. In this paper, we discuss some recent developments of this transform and illustrate how to use this transform in extreme value analysis. We also summarize the applications of excess wealth order in reliability theory, auction theory, and actuarial science. Some new research directions are mentioned as well.

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Bibliography

  1. Balakrishnan, N. and Rao, C. R.: Order Statistics: Theory and Methods. Amsterdam: Elsevier (1998)

    Google Scholar 

  2. Balakrishnan, N. and Rao, C. R.: Order Statistics: Applications. Amsterdam: Elsevier (1998)

    MATH  Google Scholar 

  3. Barlow, R. E. and Campo, R.: Total time on test processes and applications to failure data analysis. Reliability and Fault Tree Analysis (edited by R. E. Barlow, J. B. Fussell, and N. D. Singpurwalla), SIAM, Philadephia, 451–481 (1975)

    Google Scholar 

  4. Barlow, R. E., Bartholomew, D. J., Bremner, J. M. and Brunk, H. D.: Statistical Inference Under Order Restrictions. John Wiley, New York (1972)

    MATH  Google Scholar 

  5. Barrett, G. and Donald, S.: Consistent Tests for Stochastic Dominance. Econometrica, 71, 71–104 (2003)

    MathSciNet  MATH  Google Scholar 

  6. Belzunce, F., Pinar, J. F. and Ruiz, J. M.: A family of tests for right spread order. Statistics and Probability Letters, 54, 79–92 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bergman, B.: On age replacement and the total time on test concept. Scandinavian Journal of Statistics, 6, 161–168 (1979)

    MathSciNet  MATH  Google Scholar 

  8. Das, B. and Ghosh, S.: Weak limits of exploratory plots in Extreme Value Analysis. Bernoulli, to appear (2012)

    Google Scholar 

  9. David, H. A. and Nagaraja, H. N.: Order statistics (3rd ed). Wiley, New York (2003)

    Book  MATH  Google Scholar 

  10. Davison, A. C. and Smith, R. L.: Models for exceedances over high thresholds (with discussion). Journal of the Royal Statistical Society, Series B, 52, 393–442 (1990)

    MathSciNet  MATH  Google Scholar 

  11. Denuit, M., Dhaene, J., Goovaerts, M. J. and Kaas, R.: Actuarial Theory for Dependent Risks – Measures, Orders and Models. Wiley, New York (2005)

    Book  Google Scholar 

  12. Denuit, M., Goderniaux, A.-C. and Scaillet, O.: A Kolmogorov-Smirnov type test for shortfall dominance against parametric alternatives. Technometrics, 49, 88–99 (2007)

    Article  MathSciNet  Google Scholar 

  13. Embrechts, P., Kluppelberg, C. and Mikosch, T.: Modelling Extreme Events for Insurance and Finance. Springer-Verlag, Berlin (1997)

    Book  Google Scholar 

  14. Fernández-Ponce, J. M., Kochar, S. C. and Muñoz-Perez, J.: Partial orderings of distributions based on right-spread functions. Journal of Applied Probability, 35, 221–228 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ghosh, S. and Resnick, S. I.: A discussion on mean excess plots. Stochastic Processes and their Applications, 120 1492–1517 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hu, T., Chen, J. and Yao, J.: Preservation of the location independent risk order under convolution. Insurance: Mathematics and Economics, 38, 406–412 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Klefsjö, B.: TTT-plotting — a tool for both theoretical and practical problems. Journal of Statistical Planning and Inference, 29, 111–124 (1991)

    MathSciNet  Google Scholar 

  18. Kochar, S. C., Li, X. and Shaked, M.: The total time on test transform and the excess wealth stochastic order of distributions. Advances in Applied Probability, 34, 826–845 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kochar, S. C., Li, X. and Xu, M.: Excess wealth order and sample spacings. Statistical Methodology, 4, 385–392 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kochar, S. C. and Xu, M.: Comparisons of parallel systems according to the convex transform order. Journal of Applied Probability, 46, 342–352 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kochar, S. C. and Xu, M.: On the right spread order of convolutions of heterogeneous exponential random variables. Journal of Multivariate Analysis, 101, 165–176 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kochar, S. C. and Xu, M.: Stochastic comparisons of spacings from heterogeneous samples. (Martin Wells and Ashis Sengupta edited) Festschrift Volume for Sreenivasa Rao Jammalamadaka, 113–129, Springer (2011)

    Google Scholar 

  23. Kochar, S. C. and Xu, M.: On the skewness of order statistics in the multiple-outlier models. Journal of Applied Probability, 48, 271–284 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kochar, S. C. and Xu, M.: The tail behavior of the convolutions of Gamma random variables. Journal of Statistical Planning and Inference, 141, 418–428 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kochar, S. C. and Xu, M.: Some unified results on comparing linear combinations of independent gamma random variables. Probability in Engineering and Information Sciences, 26, 393–404 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. Krishna, V.: Auction theory. Academic Press, New York (2010)

    Google Scholar 

  27. Li, X.: A note on the expected rent in auction theory. Operations Research Letters, 33, 531–534 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Marshall, A. W., Olkin, I. and Arnold, B. C.: Inequalities: Theory of Majorization and Its Applications. Springer, New York (2011)

    Book  MATH  Google Scholar 

  29. Müller, A. and Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, Chichester (2002)

    MATH  Google Scholar 

  30. Resnick, S. I.: Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer, New York (2007)

    MATH  Google Scholar 

  31. Shaked, M. and Shanthikumar, J. G.: Two variability orders. Probability in the Engineering and Informational Sciences, 12, 1–23 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  32. Shaked, M. and Shanthikumar, J. G.: Stochastic orders and their applications (Second Edition). Springer Series in Statistics. Springer-Verlag, New York (2007)

    Google Scholar 

  33. Sordo, M. A.: Comparing tail variabilities of risks by means of the excess wealth order. Insurance: Mathematics and Economics, 45, 466–469 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Zhao, P., Li, X. and Da, G.: Right spread order of the second order statistics from heterogeneous exponential distributions. Communications in Statistics - Theory and Methods, 47, 3070–3081 (2011)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, USA

    Subhash Kochar

  2. Department of Mathematics, Illinois State University, Normal, IL, USA

    Maochao Xu

Authors
  1. Subhash Kochar
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  2. Maochao Xu
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Corresponding author

Correspondence to Maochao Xu .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Washington State University, Lighty 370, Pullman, 99164, Washington, USA

    Haijun Li

  2. Xiamen University, Xiamen, 361000, China, People's Republic

    Xiaohu Li

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Kochar, S., Xu, M. (2013). Excess Wealth Transform with Applications. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_14

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