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For this purpose, the BM based on using a binomial distribution is expanded to include a discrete latent variable.
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The sample is drawn without replacement, so, strictly speaking, the binomial distribution is not applicable.
The binomial distribution is now a conditional probability, given the value of r.
A standardized binomial distribution is a binomial distribution scaled and translated so that it has zero mean and unit variance.
Thus, the binomial distribution is a generalization of the Bernoulli distribution.
Binomial distribution is a fundamental statistical assumption about sampling process.
Therefore, the binomial distribution is a conservative model for the sampling process.
An extension of the binomial distribution is the beta-binomial distribution.
A Bernoulli (binomial) distribution was used for presence/absence models and a Poisson distribution for count models.
Negative binomial distribution was used for curve fitting.
Also, note that k* values obtained from binomial distribution are smaller than from hypergeometric distribution.
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