Strategies for Efficient Computation of Multivariate Poisson Probabilities

The main reason for the limited use of multivariate discrete models is the difficulty in calculating the required probabilities. The task is usually undertaken via recursive relationships which become quite computationally demanding for high dimensions and large values. The present paper discusses e...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2004-01, Vol.33 (2), p.271-292
Main Authors: Tsiamyrtzis, Panagiotis, Karlis, Dimitris
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
Mathematics
Multivariate analysis
Multivariate discrete distributions
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Panjer's family of distributions
Primary 62E99
Probability and statistics
Probability theory and stochastic processes
Recurrence relationships
Sciences and techniques of general use
Secondary 62P05
Statistics
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Summary:The main reason for the limited use of multivariate discrete models is the difficulty in calculating the required probabilities. The task is usually undertaken via recursive relationships which become quite computationally demanding for high dimensions and large values. The present paper discusses efficient algorithms that make use of the recurrence relationships in a manner that reduces the computational effort and thus allow for easy and cheap calculation of the probabilities. The most common multivariate discrete distribution, the multivariate Poisson distribution is treated. Real data problems are provided to motivate the use of the proposed strategies. Extensions of our results are discussed. It is shown that probabilities, for a large family of multivariate distributions, can be computed efficiently via our algorithms.
ISSN:0361-0918
1532-4141
DOI:10.1081/SAC-120037235