Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family

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Extended Poisson–Tweedie: Properties and regression models for count data (2016, background): “Zhu and Joe (2009) discussed the analysis of heavy-tailed count data based on the generalized PIG family, which corresponds to Poisson–Tweedie distributions with power parameter larger than 2.”
Integer-valued Lévy processes and low latency financial econometrics (2012, methodology): “This distribution was derived using a different approach by Zhu and Joe (2009), who call it a ‘generalised Poisson-inverse Gaussian family’.”