References
- Arnold, B. C. 2014. Univariate and multivariate pareto models. Journal of Statistical Distributions and Applications 1:11.
- Beare, B. K. 2009. A generalization of hoeffding’s lemma, and a new class of covariance inequalities. Statistics and Probability Letters 79:637–42.
- Block, H. W., and Z. Fang. 1988. A multivariate extension of Hoeffding’s lemma. The Annals of Probability 16:1803–20.
- Chakraborti, S., F. Jardim, and E. Epprecht. 2018. Higher order moments using the survival function: The alternative expectation formula. To appear in The American Statistician. doi:10.1080/00031305.2017.135674.
- Cuadras, C. M. 2002. On the covariance between functions. Journal of Multivariate Analysis 81:19–27.
- Feller, W. 1966. An introduction to probability theory and its applications, 2nd ed., vol.II. New York: Wiley.
- Hoeffding, W. 1940. Masstabinvariante Korrelationstheorie. Schriften des Mathematischen Instituts und Instituts für Angewandte Mathematik der Universität Berlin, vol.5, 181–233. Scale-invariant correlation theory, trans. D. Quade. 1994. In The collected works of Wassily Hoeffding, eds. N. I. Fisher and P. K. Sen, 57–107. New York: Springer.
- Hoel, P. G., S. C. Port, and C. J. Stone. 1971. Introduction to probability theory. Boston, MA: Houghton Mifflin.
- Hong, L. 2012. A remark on the alternative expectation formula. The American Statistician 66:232–3.
- Hong, L. 2015. Another remark on the alternative expectation formula. The American Statistician 69:157–9.
- Karlin, S., and H. M. Taylor. 1975. A first course in stochastic processes, 2nd ed. San Diego, CA: Academic Press.
- Kotz, S., N. Balakrishnan, and N. L. Johnson. 2000. Continuous multivariate distributions. Vol. 1 of Models and applications, 2nd ed. New York: Wiley.
- Kwong, H. S., and S. Nadarajah. 2018. Expectation formulas for integer valued multivariate random variables. Communications in Statistics – Theory and Methods 47:5514–8.
- Laha, R. G., and V. K. Rohatgi. 1979. Probability theory. New York: Wiley.
- Lo, A. 2017. Functional generalizations of Hoeffding’s covariance lemma and a formula for Kendall’s tau. Statistics and Probability Letters 122:218–26.
- Mardia, K. V. 1967. Some contributions to contingency-type bivariate distributions. Biometrika 54:235–49.
- Mardia, K. V., and J. W. Thompson. 1972. Unified treatment of moment-formulae. Sankhyā, A 34:121–32.
- Nadarajah, S., and K. Mitov. 2003. Product moments of multivariate random vectors. Communications in Statistics – Theory and Methods 32:47–60.
- Rohatgi, V. K., and A. K. Md. E. Saleh. 2015. An introduction to probability theory and mathematical statistics. 3rd ed. New York: Wiley.
- Ross, S. 2014. A first course in probability. 9th ed. Boston, MA: Pearson.
- Sen, P. K. 1994. The impact of Wassily Hoeffding’s research on nonparametrics. In The collected works of Wassily Hoeffding, eds. N. I. Fisher and P. K. Sen, 29–55. New York: Springer.