# A generalized geometric distribution and some of its properties

*Andreas N. Philippou*,
*Costas Georghiou* and
*George N. Philippou*

*Statistics & Probability Letters*, 1983, vol. 1, issue 4, 171-175

**Abstract:**
A generalized geometric distribution is introduced and briefly studied. First it is noted that it is a proper probability distribution. Then its probability generating function, mean and variance are derived. The probability distribution of the sum Yr of r independent random variables, distributed as generalized geometric, is derived. Finally, sufficient conditions are presented under which we can derive the limiting distribution of Yr - kr as r --> [infinity].

**Keywords:** Generalized; geometric; distribution; probability; generating; function; mean; variance; generalized; negative; binomial; distribution; generalized; Poisson; distribution (search for similar items in EconPapers)

**Date:** 1983

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