https://orcid.org/0000-0002-6279-3662
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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.
Acknowledgments
The authors gratefully acknowledge the constructive comments offered by the referees. Their comments improve the quality of the paper significantly.
Supporting Information: Additional information for this article is available.
Supplement: Some proofs of the article.
Mathematica folder: Mathematica codes used in the article.
R folder: R codes used in the article.
Additional information
Funding
This work was supported by the Fundamental Research Funds for the Central Universities (CQDXWL-2012-004; 106112016CDJXY100002), China Scholarship Council (201606055028), National Natural Science Foundation of China (11671060), and MOE project of Humanities and Social Sciences on the west and the border area (14XJC910001).
