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The American Statistician Volume 73, 2019 - Issue 4
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Teacher’s Corner

Demystifying the Integrated Tail Probability Expectation Formula

Ambrose LoDepartment of Statistics and Actuarial Science, The University of Iowa, Iowa City, IAView further author information
Pages 367-374 | Received 01 Feb 2018, Published online: 25 Sep 2018

References

  • Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., and Nesbitt, C. J. (1997), Actuarial Mathematics (2nd ed.), Schaumburg, IL: The Society of Actuaries.
  • Casella, G., and Berger, R. L. (2002), Statistical Inference (2nd ed.), Pacific Grove, CA: Duxbury.
  • Chakraborti, S., Jardim, F., and Epprecht, E. (2017), “Higher Order Moments Using the Survival Function: The Alternative Expectation,” The American Statistician, DOI: 10.1080/00031305.2017.1356374.
  • Cuadras, C. M. (2002), “On the Covariance between Functions,” Journal of Multivariate Analysis, 81, 19–27.
  • Denuit, M., Dhaene, J., Goovaerts, M., and Kaas, R. (2005), Actuarial Theory for Dependent Risks: Measures, Orders and Models, Chichester, UK: Wiley.
  • Hoeffding, W. (1940), “Masstabinvariante Korrelationstheorie,” Schriften des Mathematischen Instituts und des Instituts für Angewandte Mathematik der Universität Berlin, 5, 181–233.
  • Hogg, R. V., McKean, J. W., and Craig, A. T. (2013), Introduction to Mathematical Statistics (7th ed.), Boston, MA: Pearson.
  • Hong, L. (2012), “A Remark on the Alternative Expectation Formula,” The American Statistician, 66, 232–233.
  • —–— (2015), “Another Remark on the Alternative Expectation Formula,” The American Statistician, 69, 157–159.
  • Lieb, E. H., and Loss, M. (2001), Analysis (2nd ed.), Providence, RI: American Mathematical Society.
  • Lo, A. (2017), “Functional Generalizations of Hoeffding's Covariance Lemma and a Formula for Kendall's Tau,” Statistics and Probability Letters, 122, 218–226.
  • Mardia, K. V. (1967), “Some Contributions to Contingency-Type Bivariate Distributions,” Biometrika, 54, 235–249.
  • Marshall, A. W., and Olkin, I. (1967), “A Multivariate Exponential Distribution,” Journal of the American Statistical Association, 62, 30–44.
  • Müller, A., and Stoyan, D. (2002), Comparison Methods for Stochastic Models and Risks, Chichester, UK: Wiley.
  • Rényi, A. (2007), Probability Theory, Dover Publications.
  • Shea, G. A. (1983), “Hoeffding's Lemma,” in Encyclopedia of Statistical Sciences, eds. S. Kotz, N. Balakrishnan, C. Read, and B. Vidakovic, New York: Wiley.
  • Wackerly, D. D., Mendenhall, W., and Scheaffer, R. L. (2008), Mathematical Statistics with Applications (7th ed.), Belmont, CA: Thomson.

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