Journal of Applied Probability

Exact boundaries in sequential testing for phase-type distributions

Hansjörg Albrecher, Peiman Asadi, and Jevgenijs Ivanovs

Abstract

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. Exact decision boundaries for given type-I and type-II errors are derived 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 with 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 tails.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 347-358.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528485

Digital Object Identifier
doi:10.1239/jap/1417528485

Mathematical Reviews number (MathSciNet)
MR3317368

Zentralblatt MATH identifier
1309.62140

Subjects
Primary: 62L12: Sequential estimation
Secondary: 91B30: Risk theory, insurance

Keywords
Sequential probability ratio test Markov additive process scale function two-sided exit problem Esscher transform

Citation

Albrecher, Hansjörg; Asadi, Peiman; Ivanovs, Jevgenijs. Exact boundaries in sequential testing for phase-type distributions. J. Appl. Probab. 51A (2014), 347--358. doi:10.1239/jap/1417528485. https://projecteuclid.org/euclid.jap/1417528485


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