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If a random variable having a standardized binomial distribution is scaled by σ, then its variance is σ 2. The BinoGM is constructed using a mixture of standard normal distributions along the main axes, with mixture component means and weights selected using a scaled binomial distribution.
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A standardized binomial distribution is a binomial distribution scaled and translated so that it has zero mean and unit variance.
On the log scale the relationship between the mean and the variance in the Negative Binomial distribution is roughly linear for large mean counts.
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.
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.
The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k.
An extension of the binomial distribution is the beta-binomial distribution.
Negative binomial distribution was used for curve fitting.
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