Open Access
2023 Efficient sampling from the PKBD distribution
Lukas Sablica, Kurt Hornik, Josef Leydold
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Electron. J. Statist. 17(2): 2180-2209 (2023). DOI: 10.1214/23-EJS2149


In this paper we present and analyze random number generators for the Poisson Kernel-Based Distribution (PKBD) on the sphere. We show that the only currently available sampling scheme presented in Golzy and Markatou (2020) can be improved by a better selection of hyper-parameters but still yields an unbounded rejection constant as the concentration parameter approaches 1. Furthermore, we introduce two additional and superior sampling methods for which boundedness in the above mentioned case can be obtained. The first method proposes initial draws from angular central Gaussian distribution and offers uniformly bounded rejection constants for a significant part of the PKBD parameter space. The second method uses adaptive rejection sampling and the results of Ulrich (1984) to sample from the projected Saw distribution (Saw, 1978). Finally, both new methods are compared in a simulation study.


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Lukas Sablica. Kurt Hornik. Josef Leydold. "Efficient sampling from the PKBD distribution." Electron. J. Statist. 17 (2) 2180 - 2209, 2023.


Received: 1 July 2022; Published: 2023
First available in Project Euclid: 2 October 2023

MathSciNet: MR4649038
Digital Object Identifier: 10.1214/23-EJS2149

Keywords: PKBD distribution , Poisson kernel , rejection sampling , sampling , simulation , spherical distributions

Vol.17 • No. 2 • 2023
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