On the probability density function of the Hartman-Watson distribution

Tibor Pogány, Saralees Nadarajah


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.


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

Full Text:


ISSN: 1331-0623 (Print), 1848-8013 (Online)