Estimating tail probabilities of random sums of infinite mixtures of phase-type distributions

Yao, Hui, Rojas-Nandayapa, Leonardo and Taimre, Thomas (2017). Estimating tail probabilities of random sums of infinite mixtures of phase-type distributions. In: Proceedings - Winter Simulation Conference. 2016 Winter Simulation Conference, WSC 2016, Arlington, VA, United States, (347-358). 11 - 14 December 2016. doi:10.1109/WSC.2016.7822102


Author Yao, Hui
Rojas-Nandayapa, Leonardo
Taimre, Thomas
Title of paper Estimating tail probabilities of random sums of infinite mixtures of phase-type distributions
Conference name 2016 Winter Simulation Conference, WSC 2016
Conference location Arlington, VA, United States
Conference dates 11 - 14 December 2016
Convener IEEE
Proceedings title Proceedings - Winter Simulation Conference   Check publisher's open access policy
Journal name Proceedings of the ... Winter Simulation Conference. Winter Simulation Conference   Check publisher's open access policy
Place of Publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Publication Year 2017
Sub-type Fully published paper
DOI 10.1109/WSC.2016.7822102
Open Access Status Not yet assessed
ISBN 9781509044863
9781509044849
9781509044856
9781509044870
ISSN 0891-7736
1558-4305
Start page 347
End page 358
Total pages 12
Collection year 2018
Language eng
Abstract/Summary We consider the problem of estimating tail probabilities of random sums of infinite mixtures of phase-Type (lMPH) distributions -A class of distributions corresponding to random variables which can be represented as a product of an arbitrary random variable with a classical phase-Type distribution. Our motivation arises from applications in risk and queueing problems. Classical rare-event simulation algorithms cannot be implemented in this setting because these typically rely on the availability of the CDF or the MGF, but these are difficult to compute or not even available for the class of IMPH distributions. In this paper, we address these issues and propose alternative simulation methods for estimating tail probabilities of random sums of IMPH distributions; our algorithms combine importance sampling and conditional Monte Carlo methods. The empirical performance of each method suggested is explored via numerical experimentation.
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Conference Paper
Collections: School of Mathematics and Physics
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