Distinguishing Between Binomial, Hypergeometric and Negative Binomial Distributions

On Hypergeometric Generalized Negative Binomial Distribution

Confidence Bounds & Intervals for Parameters Relating to the Binomial, Negative Binomial, Poisson and Hypergeometric Distributions With Applications to Rare Events

We present here by direct argument the classical Clopper-Pearson (1934) “exact” confidence bounds and corresponding intervals for the parameter p of the binomial distribution. The same arguments can be applied to derive confidence bounds and intervals for the negative binomial parameter p, for the Poisson parameter λ, for the ratio of two Poisson parameters, ρ = λ1/λ2, and for the parameter D o...

On the quantile transform for asymmetric binomial and hypergeometric distributions

Binomial and multinomial distributions

GENERALIZED BINOMIAL AND NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDER k BY THE/-OVERLAPPING ENUMERATION SCHEME

A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distr...