Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, With an Application to Generalized Hermite Distributions

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MODELING ABUNDANCE EFFECTS IN DISTANCE SAMPLING (2004, background): “Abundance models other than Poisson or negative binomial that allow for more flexibility in modeling overdispersion may also be considered (e.g., see Bhattacharya and Holla 1965, Agarwal et al. 2002, Puig 2003).”
Discrete dispersion models and their Tweedie asymptotics (2014, methodology): “Recently, Harremoës et al. (2010) used binomial thinning to formulate an extended Poisson convergence theorem, which they called the ”law of thin numbers”, whereas Puig (2003) and Puig & Valero (2006, 2007) have characterized discrete distributions closed under convolution and binomial thinning.”
On modeling count data: a comparison of some well-known discrete distributions (2008, methodology): “The zero-inflation index was introduced by Puig [22].”
Modelling occurrence and abundance of species when detection is imperfect (2005, background): “Abundance models other than Poisson or negative binomial that allow for more flexibility OIKOS 110:2 (2005) 355 in modeling over-dispersion may also be considered (Bhattacharya and Holla 1965, Puig 2003).”