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Biometrika 1982 69(1):261-264; doi:10.1093/biomet/69.1.261
© 1982 by Biometrika Trust
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MISCELLANEA

The true characteristic function of the F distribution

P. C. B. PHILLIPS

Cowles Foundation for Research in Economics, Yale University New Haven, Connecticut, U.S.A

Formulae that are given in the literature for the characteristic function of the F distribution are incorrect and imply that the distribution has finite moments of all orders. Correct formulae are derived and the asymptotic behaviour of the characteristic function in the neighbourhood of the origin is characterized.

Key Words: Asymptotic series • Confluent hypergeometric function • Moment • Tail probability expansion


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