The density of distributions from the Bondesson class

A Note on the Numerical Evaluation of the Hartman–Watson Density and Distribution Function

“…As already mentioned in the introduction, the Hartman-Watson law is in the Bondesson class which allows to apply a Laplace inversion algorithm specifically derived for such distributions in [4]. Furthermore, this method has the advantage that it immediately implies as a corollary a similar formula for the distribution function F r .…”

“…with arbitrary parameters a, b > 0 and M > 2/(a x), and this integral is a proper Riemannian integral, since the integrand vanishes for v ↓ 0, see [4]. Regarding the choice of the parameters, [4] have shown that a = 1/x, M = 3 is usually a good choice and we will use these parameters.…”

“…Regarding the choice of the parameters, [4] have shown that a = 1/x, M = 3 is usually a good choice and we will use these parameters. Concerning the remaining parameter b, we choose b = a.…”

“…Concerning the remaining parameter b, we choose b = a. For the evaluation of the distribution function F r , it is also shown in [4] that…”