A class of bivariate negative binomial distributions with different index parameters in the marginals

• Published in: Applied mathematics and computation Vol. 217; no. 7; pp. 3069 - 3087
• Main Authors: Ng, Choung Min, Ong, Seng-Huat, Srivastava, H.M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.12.2010; Elsevier
• Subjects: Binomials; Canonical expansions and quadrant dependence; Computer generation of bivariate samples; Computer simulation; Correlation analysis; Exact sciences and technology; Extension of trivariate reduction; Mathematical analysis; Mathematical models; Mathematics; Meixner class of polynomials and Srivastava’s triple hypergeometric series; Mixed Poisson distribution; Multivariate extensions and goodness-of-fit; Numerical analysis; Numerical analysis. Scientific computation; Quadrants; Samples; Sciences and techniques of general use; Special functions; Statistical analysis; Statistical modelling; Multivariate extensions and goodness-of-fit; Meixner class of polynomials and Srivastava’s triple hypergeometric series; Computer generation of bivariate samples; Extension of trivariate reduction; Mixed Poisson distribution; Canonical expansions and quadrant dependence; Polynomial; Correlation; Multivariate distribution; Srivastava's triple hypergeometric series; Numerical analysis; Applied mathematics; Distribution function; Meixner class of polynomials and
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.08.040

In this paper, we consider a new class of bivariate negative binomial distributions having marginal distributions with different index parameters. This feature is useful in statistical modelling and simulation studies, where different marginal distributions and a specified correlation are required. This feature also makes it more flexible than the existing bivariate generalizations of the negative binomial distribution, which have a common index parameter in the marginal distributions. Various interesting properties, such as canonical expansions and quadrant dependence, are obtained. Potential application of the proposed class of bivariate negative binomial distributions, as a bivariate mixed Poisson distribution, and computer generation of samples are examined. Numerical examples as well as goodness-of-fit to simulated and real data are also given here in order to illustrate the application of this family of bivariate negative binomial distributions.