Comparison of Algorithms for Generating Poisson Random Vectors: A Review

by Masahiko Gosho, Kazushi Maruo.

Abstract: Multivariate correlated Poisson data are commonly analyzed in longitudinal or clustered studies. Monte Carlo simulation studies are often useful to evaluate the properties of the parameter estimator under the finite sample size when the Poisson model is fitted to such data. In this paper, we review two algorithms proposed by Sim, J Stat Comput Sim 47:1-10, (1993) and Krummenauer, Biometrical J 40:823-832, (1998), for generating the multivariate Poisson random numbers with non-identity covariance matrix. In addition, we graphically represent the range constraints for the correlation parameter of the multivariate Poisson distribution with the two algorithms. Consequently, the constraint of the algorithm proposed by Krummenauer (1998) was much stricter than that of the algorithm proposed by Sim (1993).

Key Words: Covariance Matrix, Correlation Matrix, Multivariate Poisson Random Numbers

Authors:
Masahiko Gosho, m-gosyo@kowa.co.jp
Kazushi Maruo, k-maruo@kowa.co.jp

Editor: Ravi Khattree, khattree@oakland.edu

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