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Small-t Expansion for the Hartman-Watson Distribution

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  • Dan Pirjol

    (Stevens Institute of Technology)

Abstract

The Hartman-Watson distribution with density f r ( t ) = 1 I 0 ( r ) θ ( r , t ) $f_{r}(t)=\frac {1}{I_{0}(r)} \theta (r,t)$ with r > 0 is a probability distribution defined on t ∈ ℝ + $t \in \mathbb {R}_{+}$ , which appears in several problems of applied probability. The density of this distribution is given by an integral θ(r, t) which is difficult to evaluate numerically for small t → 0. Using saddle point methods, we obtain the first two terms of the t → 0 expansion of θ(ρ/t, t) at fixed ρ > 0.

Suggested Citation

  • Dan Pirjol, 2021. "Small-t Expansion for the Hartman-Watson Distribution," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1537-1549, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09827-5
    DOI: 10.1007/s11009-020-09827-5
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    References listed on IDEAS

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