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Exemplary Multivariate Applications

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Multivariate Exponential Families: A Concise Guide to Statistical Inference

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

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Abstract

The usefulness of results for exponential families is demonstrated by means of three multivariate examples of different kind. As a discrete probability distribution, the family of negative multinomial distributions is considered, and results in parameter estimation and statistical testing are shown. The Dirichlet distribution serves as an example of continuous distributions, where maximum likelihood estimation, as well as the likelihood ratio test and the Wald test for a simple null hypothesis are addressed. Moreover, findings in exponential families are applied to generalized order statistics, which form a unifying approach to various models of ordered random variables.

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References

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Authors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Stefan Bedbur & Udo Kamps

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  1. Stefan Bedbur
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  2. Udo Kamps
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Bedbur, S., Kamps, U. (2021). Exemplary Multivariate Applications. In: Multivariate Exponential Families: A Concise Guide to Statistical Inference. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-81900-2_6

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