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Another Remark on the Alternative Expectation Formula

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  • Liang Hong

Abstract

Students in a calculus-based probability course will often see the expectation formula for nonnegative continuous random variables in terms of the survival function. This alternative expectation formula has a wide spectrum of applications. It is natural to ask whether there is a multivariate version of this formula. This note gives an affirmative answer by establishing such a formula using two different approaches. The two approaches employed in this note correspond to the two approaches for the univariate case. Supplementary materials for this article are available online.

Suggested Citation

  • Liang Hong, 2015. "Another Remark on the Alternative Expectation Formula," The American Statistician, Taylor & Francis Journals, vol. 69(3), pages 157-159, August.
    • Handle: RePEc:taf:amstat:v:69:y:2015:i:3:p:157-159
    DOI: 10.1080/00031305.2015.1049710
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    Cited by:

    1. Ogasawara, Haruhiko, 2018. "The inverse survival function for multivariate distributions and its application to the product moment," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 71-76.
    2. Piyush Kant Rai & Anu Sirohi, 2020. "Alternative approach to moments of order statistics from one-parameter Weibull distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 169-178, March.
    3. Song, Pingfan & Tan, Changchun & Wang, Shaochen, 2019. "On the moment generating function for random vectors via inverse survival function," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 345-350.
    4. Liu, Yang, 2020. "A general treatment of alternative expectation formulae," Statistics & Probability Letters, Elsevier, vol. 166(C).
    5. Rai Piyush Kant & Sirohi Anu, 2020. "Alternative approach to moments of order statistics from one-parameter Weibull distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 21(1), pages 155-162, March.

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