A1317
Title: The first-passage-time moments for Hougaard Process and its Birnbaum-Saunders approximation
Authors: Yi-Shain Dong - National Central University (Taiwan) [presenting]
Tsai-Hung Fan - National Central University (Taiwan)
Chien-Yu Peng - Academia Sinica (Taiwan)
Abstract: 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. The aim is to derive the finite moments of FPT distributions based on Hougaard processes and provide a theoretical justification for BS approximation regarding convergence rates. Further, it is shown that the first moment of the FPT distribution for a Hougaard process approximated by the BS distribution is larger and provides 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.
