國立政治大學統計學系
學 術 演 講
主講人：董奕賢助理教授(台北大學統計學系)學 術 演 講
題 目：The First-Passage-Time Moments for Hougaard Process and its Birnbaum-
Saunders Approximation
時 間：民國113年2月26日 (星期一) 下午1：30
地 點：國立政治大學逸仙樓050101教室
摘 要：
Hougaard processes, which include gamma and inverse Gaussian processes as special cases, as well as the moments of the corresponding first-passage-time (FPT) distributions, are commonly used in many applications. Because the density function of a Hougaard process involves an intractable infinite series, the Birnbaum-Saunders (BS) distribution is often used to approximate its FPT distribution. This article derives the finite moments of FPT distributions based on Hougaard processes and provides a theoretical justification for BS approximation in terms of convergence rates. Further, we show that the first moment of the FPT distribution for a Hougaard process approximated by the BS distribution is larger and provide a sharp upper bound for the difference using an exponential integral. The conditions for convergence coincidentally elucidate the classical convergence results of Hougaard distributions. Some numerical examples are proposed to support the validity and precision of the theoretical results.
This work cooperated with Tsai-Hung Fan (National Central University) and Chien-Yu Peng (Academia Sinica).Keywords: characteristic function; contour integration; exponential dispersion model; residue; Stirling numbers.
