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From the generalized gamma to the generalized negative binomial distribution. (English) Zbl 0743.62014
Summary: The generalized gamma distribution contains the gamma and the inverse Gaussian distribution as special cases. It is proposed as an alternative to the generalized inverse Gaussian distribution. Used as a mixing distribution for an unknown Poisson parameter it leads to the generalized negative binomial distribution.
MSC:
62E10Characterization and structure theory of statistical distributions
60E07Infinitely divisible distributions; stable distributions
62P05Applications of statistics to actuarial sciences and financial mathematics