Generation of Multivariate Discrete Data with Generalized Poisson, Negative Binomial and Binomial Marginal Distributions

TL;DR

This paper introduces an algorithm for generating multivariate discrete data with specified correlations and marginals following generalized Poisson, negative binomial, and binomial distributions, useful for various scientific fields.

Contribution

It extends previous frameworks by enabling the generation of correlated multivariate discrete data with flexible marginal distributions, demonstrated through simulations and real data applications.

Findings

Algorithm effectively generates correlated data with desired marginals.

Performance validated across multiple simulated and real datasets.

Potential for broad application in scientific research involving discrete data.

Abstract

The analysis of multivariate discrete data is crucial in various scientific research areas, such as epidemiology, the social sciences, genomics, and environmental studies. As the availability of such data increases, developing robust analytical and data generation tools is necessary to understand the relationships among variables. This paper builds upon previous work on data generation frameworks for multivariate ordinal data with a prespecified correlation matrix. The proposed algorithm generates multivariate discrete data from marginal distributions that follow the generalized Poisson, negative binomial, and binomial distributions. A step-by-step algorithm is provided, and its performance is illustrated in four simulated data scenarios and three real-data scenarios. This technique has the potential to be applied in a wide range of settings involving the generation of correlated discrete data.