Summary
A discrete r.v. X is generalized (compounded) by another discrete r.v. Zi to yield the compound distribution of Z = Z1+ … + ZX. Distributional properties are given concerning the bivariate structure of X and Z. The joint, marginal, and conditional distributions arising out of (X, Z) are derived via probability generating function techniques. Special attention is given to power series distributions (PSD), in particular when Z is a compound Poisson. Recurrences for joint probabilities and cumulants are indicated. Several ad hoc estimation techniques are discussed.
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© 1981 D. Reidel Publishing Company
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Cacoullos, T., Papageorgiou, H. (1981). On Bivariate Discrete Distributions Generated by Compounding. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8549-0_16
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DOI: https://doi.org/10.1007/978-94-009-8549-0_16
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