Exact boundaries in sequential testing for phase-type distributions
Probability
2013-07-24 v2
Abstract
We consider Wald's sequential probability ratio test for deciding whether a sequence of independent and identically distributed observations comes from a specified phase-type distribution or from an exponentially tilted alternative distribution. In this setting, we derive exact decision boundaries for given Type I and Type II errors by establishing a link with ruin theory. Information on the mean sample size of the test can be retrieved as well. The approach relies on the use of matrix-valued scale functions associated to a certain one-sided Markov additive process. By suitable transformations the results also apply to other types of distributions including some distributions with regularly varying tail.
Cite
@article{arxiv.1306.2783,
title = {Exact boundaries in sequential testing for phase-type distributions},
author = {Hansjörg Albrecher and Peiman Asadi and Jevgenijs Ivanovs},
journal= {arXiv preprint arXiv:1306.2783},
year = {2013}
}