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On the Poisson Approximation of the Binomial Distribution
Siberian Mathematical Journal, 2001Given two arbitrary probability distributions \(P\) and \(Q\) on the real line and an arbitrary nonnegative constant \(z\), denote by \(\rho(z,P,Q)\) the so-called Dudley distance between \(P\) and \(Q\): \[ \rho(z,P,Q)=\inf_{\xi,\eta}\mathbf{P}\{|\xi-\eta|>z\}, \] where the infimum is calculated over all random variables \(\xi\) and \(\eta\) on a ...
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negative binomial distribution
1998The negative binomial distribution is an alternative to the Poisson distribution for modeling counts. It is useful when counts show more variation than the Poisson allows (overdispersion). This article shows two ways of deriving it, one way as a waiting time distribution for a certain number of successes with binary data, and the other way as a gamma ...
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On the compound binomial distribution
Annals of the Institute of Statistical Mathematics, 1960Reiko Hayakawa, Goro Ishii
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Modeling microbial abundances and dysbiosis with beta-binomial regression
Annals of Applied Statistics, 2020Bryan D Martin +2 more
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Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models
Biometrika, 2021Ioannis Kosmidis, David Firth
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