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Alternative expectation formulas for real-valued random vectors

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  • Haruhiko Ogasawara

Abstract

When the elements of a random vector take any real values, formulas of product moments are obtained for continuous and discrete random variables using distribution/survival functions. The random product can be that of strictly increasing functions of random variables. For continuous cases, the derivation based on iterated integrals is employed. It is shown that Hoeffding’s covariance lemma is algebraically equal to a special case of this result. For discrete cases, the elements of a random vector can be non-integers and/or unequally spaced. A discrete version of Hoeffding’s covariance lemma is derived for real-valued random variables.

Suggested Citation

  • Haruhiko Ogasawara, 2020. "Alternative expectation formulas for real-valued random vectors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(2), pages 454-470, January.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:2:p:454-470
    DOI: 10.1080/03610926.2018.1543773
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    Cited by:

    1. Liu, Yang, 2020. "A general treatment of alternative expectation formulae," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. Saulius Paukštys & Jonas Šiaulys & Remigijus Leipus, 2023. "Truncated Moments for Heavy-Tailed and Related Distribution Classes," Mathematics, MDPI, vol. 11(9), pages 1-15, May.

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