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Abstract:
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In methodological and applied statistical research, the use of finite mixture models (FMMs) has received considerable attention due to its fexibility when modeling data across a wide variety of distributions with various shapes, from symmetric to left- or right-skewed, with varying kurtosis, etc. Evidently, thanks to the additional parameters involved and flexibility of shape of the resulting marginal density function, FMMs have the potential to capture many combinations of mean, variance, and higher-moment functions. Here, a general framework of discrete FMMs is proposed that flexibly handles both over- and underdispersed count data, with appealing interpretation in both of these cases. The flexibility of the proposal is twofold: (1) one can choose from a wide class of component distributions; and (2) mixture weights do not have to be all positive but certain negative values are allowed as well. As result, a wide variety of dispersed regions can be modelled. Applying the approach to an underdispersed demographic setting shows important improvement in goodness-of-fit compared to existing models. Negative weights are achieved to accommodate the underdispersed nature of the data.
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