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Multivariate finite-support phase-type distributions

Part of: Sampling theory, sample surveys Markov processes Special processes Distribution theory - Probability

Published online by Cambridge University Press:  23 November 2020

Celeste R. Pavithra  and
T. G. Deepak Open the ORCID record for T. G. Deepak [Opens in a new window]
Celeste R. Pavithra*
Affiliation:
IIST Thiruvananthapuram
T. G. Deepak*
Affiliation:
IIST Thiruvananthapuram
*
*Postal address: Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India.
*Postal address: Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India.
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Abstract

We introduce a multivariate class of distributions with support I, a k-orthotope in $[0,\infty)^{k}$ , which is dense in the set of all k-dimensional distributions with support I. We call this new class ‘multivariate finite-support phase-type distributions’ (MFSPH). Though we generally define MFSPH distributions on any finite k-orthotope in $[0,\infty)^{k}$ , here we mainly deal with MFSPH distributions with support $[0,1)^{k}$ . The distribution function of an MFSPH variate is computed by using that of a variate in the MPH $^{*} $ class, the multivariate class of distributions introduced by Kulkarni (1989). The marginal distributions of MFSPH variates are found as FSPH distributions, the class studied by Ramaswami and Viswanath (2014). Some properties, including the mixture property, of MFSPH distributions are established. Estimates of the parameters of a particular class of bivariate finite-support phase-type distributions are found by using the expectation-maximization algorithm. Simulated samples are used to demonstrate how this class could be used as approximations for bivariate finite-support distributions.

Keywords

Multivariate PH distributiondensenessEM algorithm

MSC classification

Primary: 60E05: Distributions 60K37: Processes in random environments
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 62D05: Sampling theory, sample surveys
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1260 - 1275
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Copyright
© Applied Probability Trust 2020

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