ON THE BESSEL DISTRIBUTION AND RELATED PROBLEMS

LIN YUAN AND JOHN D. KALBFLEISCH

Department of Statistics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

(Received October 13, 1997; revised February 9, 1999)

Abstract. This article investigates basic properties of the Bessel distribution, a power series distribution which has not been fully explored before. Links with some well-known distributions such as the von Mises-Fisher distribution are described. A simulation scheme is also proposed to generate random samples from the Bessel distribution. This scheme is useful in Bayesian inferences and Monte Carlo computation.

Key words and phrases: Bessel distribution, randomized gamma distribution, von Mises-Fisher distribution, Bessel quotient, simulation, path integral.