Simulation from the Bessel distribution with
applications
George Iliopoulos and Dimitris Karlis
The Bessel distribution, introduced recently by Yuan and Kalbfleisch (Ann.
Inst. Math. Statist., 2000), can be useful in many applications. In particular,
this distribution appears in two Bayesian estimation problems, namely,
estimation of the noncentrality parameter of a noncentral chi--square
distribution and of the parameters of Downton's bivariate exponential
distribution. Implementation of Markov chain Monte Carlo algorithms requires
generation of observations from the Bessel distribution. In this paper we
propose and compare exact simulation schemes generating Bessel variates based
on certain properties of the distribution as well as the rejection method.
AMS 2000 subject classifications: 65C10, 62F15.
Key words and phrases: Bessel distribution, simulation, rejection
method, noncentral chi--square distribution, Downton's bivariate exponential
distribution, Markov chain Monte Carlo.