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Abstract:
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In this paper, we develop a class of bivariate discrete distributions following the approach of Kundu(2018). Kundu takes each marjginal as the geometric sum of a baseline distribution. We replace the geometric distribution with Generalized Hurwitz-Lerch zeta distribution (GHLZD) which includes logseries and Reimann Zeta as special cases (Gupta et. al (2008)). These distributions provide alternatives to Kundu's recently developed families. We develop forms of probability function (pf), probability generating function (pgf), and cross moments. Subsequently, we replace GLHZD with logseries and develop bivariate distributions such as bivariate Poisson-logseries, bivariate binomial-logseries and bivariate negative binomial-logseries. For these distribution, we present closed-form expressions for bivariate pf and cross moments, noting the presence of over- and/or under-dispersion. We propose two methods of estimation: method of moments (MM) and method of maximum likelihood (MLE) along with some numerical examples from the literature and compare the results. We also obtain the information matrix for the three models and compare the asymptotic relative efficiencies of the MM and the MLE.
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