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Note on a relation between the distribution functions and characteristic functions

✍ Scribed by Minoru Motoo

Publisher
Springer Japan
Year
1954
Tongue
English
Weight
136 KB
Volume
6
Category
Article
ISSN
0020-3157

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πŸ“œ SIMILAR VOLUMES

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✍ I. Dreier; S. Kotz πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 71 KB

Utilizing the theory of positive deΓΏnite densities we express the density of a t-random variable as the characteristic function of a convolution of two Gamma-variables. This allows us to obtain a simple interpretation and an expression for the characteristic function of the t-variable.

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Li [i] evaluates characteristic functions of two spherical matrix distributions in terms of zonal polynomials. The present paper evaluates these characteristic functions explicitly in terms of known multiple series without using zonal polynomials.