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Format: VoseBetaNegBin(s, a, b, U)
The Beta-Negative Binomial(s, a, b) distribution models the number of failures that will occur in a binomial process before s successes are observed and where the binomial probability p is itself a random variable taking a Beta(a, b) distribution.
Thus the Beta-Negative Binomial distribution has the same relationship to the BetaBinomial distribution as the Negative Binomial distribution is to the Binomial.
When modeling or analyzing counting data, it is often desirable to modify probability of zero of the discrete distribution we use, to more accurately model the probability of "no event occurring". We can make two types of modifications to our distribution for this:
Zero-inflated model - we increase the probability of zero. (equations)
Zero-truncated model - we entirely remove the probability of zero events occurring. (equations)
See also: Zero-modified counting distributions
VoseBetaNegBin generates values from this distribution or calculates a percentile
VoseBetaNegBinObject constructs a distribution object for this distribution
VoseBetaNegBinProb returns the probability density or cumulative distribution function for this distribution
VoseBetaNegBinProb10 returns the log10 of the probability density or cumulative distribution function
VoseBetaNegBitFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution
VoseBetaNegBinFitObject constructs a distribution object of this distribution fitted to data
VoseBetaNegBinFitP returns the parameters of this distribution fitted to data
