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A discrete distribution arising as a solution of a linear difference equation: Extension of the non central negative binomial distribution. (English) Zbl 1162.62006
Summary: This article considers a discrete distribution that arises as the dominant solution of a linear difference equation. Basic properties and various chance mechanisms that lead to this distribution are given. In particular, its formulation as a weighted distribution and a mixed Poisson process are proposed. Parameter estimation by (a) using a combination of observed frequencies and moments and (b) maximum likelihood are examined. An example of goodness of fit is considered.

MSC:
62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation
39A10 Additive difference equations
60E05 Probability distributions: general theory
33C90 Applications of hypergeometric functions
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