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Exact boundaries in sequential testing for phase-type distributions

Part of: Mathematical economics Sequential methods

Published online by Cambridge University Press:  30 March 2016

Hansjörg Albrecher ,
Peiman Asadi  and
Jevgenijs Ivanovs
Hansjörg Albrecher
Affiliation:
University of Lausanne and Swiss Finance Institute, Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, 1015 Lausanne, Switzerland. Email address: hansjoerg.albrecher@unil.ch.
Peiman Asadi
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, 1015 Lausanne, Switzerland. Email address: peiman.asadi@unil.ch.
Jevgenijs Ivanovs
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, 1015 Lausanne, Switzerland. Email address: jevgenijs.ivanovs@unil.ch.
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Abstract

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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.

Keywords

Sequential probability ratio testMarkov additive processscale functiontwo-sided exit problemEsscher transform

MSC classification

Primary: 62L12: Sequential estimation
Secondary: 91B30: Risk theory, insurance
Type
Part 8. Markov processes and renewal theory
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 347 - 358
Copyright
Copyright © Applied Probability Trust 2014 

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