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Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments

Author

Listed:
  • Hong-Jiang Wu

    (Chongqing University)

  • Ying-Ying Zhang

    (Chongqing University
    Chongqing University)

  • Han-Yu Li

    (Chongqing University
    Chongqing University)

Abstract

Inspired by the Conjugate Variables Theorem in physics, we provide a general expectation identity for univariate continuous random variables by utilizing integration by parts. We then apply the general expectation identity to some common univariate continuous random variables (normal, gamma (including chi-square and exponential), beta, double exponential, F, inverse gamma, logistic, lognormal, Pareto, t, uniform, and Weibul) and obtain their specific expectation identities from the general expectation identity. After that, we use the specific expectation identities to derive high-order moments of the corresponding univariate continuous random variables.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01329-5
    DOI: 10.1007/s00362-022-01329-5
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    References listed on IDEAS

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