A general method is proposed for testing the fit to any member of the invariant under convolutions family of count models, parameterized by mean and variance. The test statistics, which are of the ...

Operator methods in probability: generating functions, moment generating functions, Laplace transforms, and characteristic functions. Notions of convergence: convergence in probability and weak laws ...

This paper deals with the simple Galton-Watson process with immigration, {Xn} with offspring probability generating function (p.g.f.)F (s) and immigration p.g.f. B (s), under the basic assumption that ...