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Simulating select families of multivariate discrete variates with positive correlations

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Procedures for simulating multivariate discrete distributions are often needed for modeling real‐life situations. Several authors have provided algorithms to simulate data from such distributions, yet the need for algorithms that produce multivariate discrete correlated variates persists. Thus, we propose a simple algorithm to simulate values from several multivariate discrete distributions with positive correlations. The algorithm samples from the mixture distribution that arises from a suitable two‐level hierarchical structure. Our algorithm is computationally efficient, straightforward to implement, and produces values with any positive correlation in (0,1). We illustrate our proposal through two trivariate examples implemented in R. This article is categorized under: Algorithms and Computational Methods > Random Number Generation
Simulated sample of size 50 from a three‐variate Poisson distribution with expected value 2 for each Xj and pairwise correlation of 0.9. Bubble plots in the upper right panel and bubble qq‐plots in the lower left panel.
[ Normal View | Magnified View ]
Simulated sample of size 400 from a three‐variate negative binomial distribution with 450 fixed successes and success probability of 0.5 for each Xj, and pairwise correlation 0.5. Bubble plots in the upper right panel and bubble qq‐plots in the lower left panel.
[ Normal View | Magnified View ]
Simulated sample of size 400 from a three‐variate negative binomial distribution with four fixed successes and success probability of 0.5 for each Xj, and pairwise correlation 0.5. Bubble plots in the upper right panel and bubble qq‐plots in the lower left panel.
[ Normal View | Magnified View ]

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Algorithms and Computational Methods > Random Number Generation

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