Exact boundaries in sequential testing for phase-type distributions

Hansjörg Albrecher; Peiman Asadi; Jevgenijs Ivanovs

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arXiv · 1306.2783

Exact boundaries in sequential testing for phase-type distributions

Hansjörg Albrecher·Peiman Asadi·Jevgenijs Ivanovs

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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.

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BibTeX RIS

Hansjörg Albrecher, Peiman Asadi, Jevgenijs Ivanovs. 2013-07-23. Exact boundaries in sequential testing for phase-type distributions. https://arxiv.org/abs/1306.2783

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