𝑞-probability distributions via an extension of the Bernoulli process

Feinsilver, Philip

doi:10.1090/S0002-9939-1983-0684648-5

$q$-probability distributions via an extension of the Bernoulli process
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Proc. Amer. Math. Soc. 87 (1983), 508-515 Request permission

Abstract:

One-parameter extensions of the Binomial, Negative Binomial, Poisson, Geometric and Gamma distributions are derived via an extension of the standard Bernoulli counting scheme. The method is to examine the elementary "potential theory" for the basic process. Some interesting extensions to continuous time are mentioned also.

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