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Research Report SRR95-044
The characteristic function of The Student t distribution
Simon Hurst
Abstract:
This paper derives a simple analytic expression for the characteristic
function of the Student t distribution for all degrees of freedom
\nu \geq 0. The Student t distribution is a particular case of
the
symmetric generalised hyperbolic distribution. The method of
subordination is used here to obtain a derivation of the
characteristic function of the symmetric generalised hyperbolic
distribution. The characteristic function of the Student t
distribution is then obtained via the characteristic function of the
symmetric generalised hyperbolic distribution. It involves the
modified Bessel function of the third kind.
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