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The Characteristic Function of the Dirichlet and Multivariate F Distributions

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Abstract

Formulae are derived for the characteristic function of the inverted Dirichlet distribution and hence the multivariate F. The analysis involves a new function with multiple arguments that extends the confluent hypergeometric function of the second kind. This function and its properties are studied in the paper and a simple integral representation is given which is useful for numerical work. A special case connected with the multivariate t distribution is also explored.

Suggested Citation

  • Peter C.B. Phillips, 1988. "The Characteristic Function of the Dirichlet and Multivariate F Distributions," Cowles Foundation Discussion Papers 865, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:865
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d08/d0865.pdf
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    1. Anderson, T W & Sawa, Takamitsu, 1973. "Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions," Econometrica, Econometric Society, vol. 41(4), pages 683-714, July.
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    Cited by:

    1. Ashraf Gouda & Tamás Szántai, 2010. "On numerical calculation of probabilities according to Dirichlet distribution," Annals of Operations Research, Springer, vol. 177(1), pages 185-200, June.
    2. M. Ghorbel & M. Farah, 2015. "Dirichlet partition on symmetric matrices," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(1), pages 73-83, February.

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