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Expectation identity for the binomial distribution and its application in the calculations of high-order binomial moments

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  • Ying-Ying Zhang
  • Teng-Zhong Rong
  • Man-Man Li

Abstract

For the exponential families normal, gamma, beta, Poisson, and negative binomial, there exists an expectation identity for each of the family. For the binomial family, we discover an expectation identity, which is useful in analytical calculations of its high-order moments.

Suggested Citation

  • Ying-Ying Zhang & Teng-Zhong Rong & Man-Man Li, 2019. "Expectation identity for the binomial distribution and its application in the calculations of high-order binomial moments," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(22), pages 5467-5476, November.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:22:p:5467-5476
    DOI: 10.1080/03610926.2018.1435818
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    Cited by:

    1. Hong-Jiang Wu & Ying-Ying Zhang & Han-Yu Li, 2023. "Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments," Statistical Papers, Springer, vol. 64(2), pages 477-496, April.

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