Doubly inflated Poisson model using Gaussian copula |
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| Authors: | Sumen Sen Pooja Sengupta Norou Diawara |
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| Affiliation: | 1. Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN, USA;2. Quantitative methods, International Management Institute, Kolkata, India;3. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, USA |
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| Abstract: | Multivariate data are present in many research areas. Its analysis is challenging when assumptions of normality are violated and the data are discrete. The Poisson discrete data can be thought of as very common discrete type, but the inflated and the doubly inflated correspondence are gaining popularity (Sengupta, Chaganty, and Sabo 2015; Lee, Jung, and Jin 2009; Agarwal, Gelfand, and Citron-Pousty 2002). Our aim is to build a statistical model that can be tractable and used to estimate the model parameters for the multivariate doubly inflated Poisson. To keep the correlation structure, we incorporate ideas from the copula distributions. A multivariate doubly inflated Poisson distribution using Gaussian copula is introduced. Data simulation and parameter estimation algorithms are also provided. Residual checks are carried out to assess any substantial biases. The model dimensionality has been increased to test the performance of the provided estimation method. All results show high-efficiency and promising outcomes in the modeling of discrete data and particularly the doubly inflated Poisson count type data, under a novel modified algorithm. |
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| Keywords: | Copula Gaussian copula inflated Poisson. |
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