Multivariate zero-inflated Bell distribution and its inference and applications

• Published in: Applied Mathematical Modelling 2022-03, Vol.103, p.543-556
• Main Author: Lemonte, Artur J.
• Format: Article
• Language: English
• Subjects: Algorithms; Excess zeros; Expectation-maximization algorithm; Generalized poisson distribution; Maximum likelihood estimates; Maximum likelihood estimation; Maximum likelihood estimators; Multivariate analysis; Multivariate count data; Parameter estimation; Poisson distribution
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.11.001

•Multivariate count data modeling.•Multivariate count data with excess zeros.•Parametric multivariate zero-inflated distributions.•Multivariate zero-inflated Bell distribution. In this paper we introduce a multivariate family of distributions for multivariate count data with excess zeros, which is a multivariate extension of the univariate zero-inflated Bell distribution. We derive various general properties of this multivariate distribution. In particular, the marginal distributions are univariate zero-inflated Bell distributions. The model parameters are estimated using the traditional maximum likelihood estimation method. In addition, we develop a simple EM algorithm to compute the maximum likelihood estimates of the parameters of the new multivariate distribution with closed-form expressions for the maximum likelihood estimators. Empirical applications that employ real multivariate count data are considered to illustrate the usefulness of the new class of multivariate distributions, and comparisons with the multivariate zero-inflated Poisson distribution, multivariate zero-adjusted Poisson distributions, and multivariate zero-inflated generalized Poisson distribution are made.