On the probability density function of the Hartman-Watson distribution

Tibor Pogány; Saralees Nadarajah

Vol. 27 No. 1 (2022)

Regular Articles

On the probability density function of the Hartman-Watson distribution

Published 2022-04-15

Tibor Pogány
Saralees Nadarajah

Tibor Pogány
Faculty of Maritime Studies, University of Rijeka, Croatia

Saralees Nadarajah
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

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Abstract

The Hartman-Watson distribution arises in many areas of applied probability. But its probability density function is difficult to compute. Recently, [13] gave the first two terms of its asymptotic expansion. Here, we derive the probability density function and a full asymptotic expansion in computable forms.

Keywords

computable series representation, Hartman-Watson distribution, Laplace-Mellin transform, parabolic cylinder function

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Author Biography

Tibor Pogány

Professor emeritus