@article { ISI:000289337100008,
	title = {Modelling species abundance using the Poisson-Tweedie family},
	journal = {Environmetrics},
	volume = {22},
	number = {2},
	year = {2011},
	month = {MAR},
	pages = {152-164},
	publisher = {Wiley-Blackwell},
	type = {Article},
	abstract = {The distribution of an organism species in the environment deviates frequently from randomness due to natural cycles, availability of food resources and avoidance of harm. As a result, observed data can show over-dispersion, zero-inflation and even heavy tail. Models such as the negative binomial (NB), Poisson-inverse Gaussian (PIG), and zero-inflated Poisson are frequently used in applications instead of the Poisson distribution which is usually the default model. This paper uses a three-parameter discrete distribution that unifies distributions such as Poisson, NB, PIG, Neyman Type A, and Poisson-Pascal. The three-parameter family covers a wide range of tail heaviness relative to NB, and thus suitable for modelling over-dispersed count data with a shorter or longer tail. Moreover, it shows some capacity for zero-inflated data. Grouped counts of coliform bacteria from Lake Erie and counts of European corn borer larvae in field corn are used to illustrate the application of the model and the associated likelihood-based inferences. Copyright (C) 2010 John Wiley \& Sons, Ltd.},
	keywords = {Count data, generalized Poisson-inverse Gaussian, Negative binomial, Neyman Type A, over-dispersion, Poisson, Poisson-Pascal, tail index, zero-inflation},
	issn = {1180-4009},
	doi = {10.1002/env.1036},
	author = {El-Shaarawi, Abdel H. and Zhu, Rong and Joe, Harry}
}
@article { ISI:000294806800005,
	title = {Weighted scores method for regression models with dependent data},
	journal = {Biostatistics},
	volume = {12},
	number = {4},
	year = {2011},
	month = {OCT},
	pages = {653-665},
	publisher = {Oxford Univ Press},
	type = {Article},
	abstract = {<p>There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a {\textquoteleft}{\textquoteleft}weighted scores method{\textquoteright}{\textquoteright}, which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our method is robust and nearly as efficient as maximum likelihood for fully specified copula models. An illustrative example is given to show the use of our weighted scores method to analyze utilization of health care based on family characteristics.</p>
},
	keywords = {Composite likelihood, Copulas, Count data, Estimating equations, Negative binomial},
	issn = {1465-4644},
	doi = {10.1093/biostatistics/kxr005},
	author = {Nikoloulopoulos, Aristidis K. and Joe, Harry and Chaganty, N. R.}
}
