@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}
}
@booklet {NSERC Canada; Hong Kong Polytechnic University; University of Saskatchewan},
	title = {A general family of limited information goodness-of-fit statistics for multinomial data},
	journal = {Dependence Modeling: Vine Copula Handbook},
	volume = {75},
	number = {3},
	year = {2010},
	month = {SEP},
	pages = {393-419},
	publisher = {Springer},
	type = {Article},
	chapter = {10},
	address = {Singapore},
	abstract = {Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, 2005; Psychometrika 71:713-732, 2006) introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi-square. The new statistics need not be based on margins, and can be used for one-dimensional multinomials. We also provide theory that explains why limited information statistics have good power, regardless of sparseness. We show how quadratic-form statistics can be constructed that are more powerful than X (2) and yet, have approximate chi-square null distribution in finite samples with large models. Examples with models for truncated count data and binary item response data are used to illustrate the theory.},
	keywords = {categorical data analysis, cell-focusing, discrete data, item response theory, overdispersion, overlapping cells, Poisson models, quadratic form statistics, Rasch models, score test, sparse contingency tables, zero-inflation},
	issn = {0033-3123},
	doi = {10.1007/s11336-010-9165-5},
	url = {{http://www.worldscibooks.com/economics/7699.html doi = 10.1142/9789814299886,  @InCollectionCooke.Joe.ea2011},
	author = {Joe, Harry and Maydeu-Olivares, Alberto},
	editor = {Kurowicka, D. and Joe, H.}
}
