Beta-Negative Binomial distribution


Format: BetaNegBin(s, a, b)

 

Uses

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 has to the Binomial.

Zero-modified versions

When modeling or analyzing counting data, it is often desirable to modify the 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.

  • Zero-truncated model - we entirely remove the probability of zero events occurring.

ModelRisk functions added to Microsoft Excel for the Beta-Negative Binomial distribution

VoseBetaNegBin generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseBetaNegBinObject constructs a distribution object for this distribution.

VoseBetaNegBinProb returns the probability mass or cumulative distribution function for this distribution.

VoseBetaNegBinProb10 returns the log10 of the probability mass 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.

 

ModelRisk functions added to Microsoft Excel for the Zero-Inflated Beta-Negative Binomial distribution

VoseZIBetaNegBin generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseZIBetaNegBinObject constructs a distribution object for this distribution.

VoseZIBetaNegBinProb returns the probability mass or cumulative distribution function for this distribution.

VoseZIBetaNegBinProb10 returns the log10 of the probability mass or cumulative distribution function.  

VoseZIBetaNegBitFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseZIBetaNegBinFitObject constructs a distribution object of this distribution fitted to data.

VoseZIBetaNegBinFitP returns the parameters of this distribution fitted to data.

 

ModelRisk functions added to Microsoft Excel for the Zero-Truncated Beta-Negative Binomial distribution

VoseZTBetaNegBin generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseZTBetaNegBinObject constructs a distribution object for this distribution.

VoseZTBetaNegBinProb returns the probability mass or cumulative distribution function for this distribution.

VoseZTBetaNegBinProb10 returns the log10 of the probability mass or cumulative distribution function.  

VoseZTBetaNegBitFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseZTBetaNegBinFitObject constructs a distribution object of this distribution fitted to data.

VoseZTBetaNegBinFitP returns the parameters of this distribution fitted to data.

 

Beta-Negative Binomial distribution equations

Zero-Inflated Beta-Negative Binomial distribution equations

Zero-Truncated Beta-Negative Binomial distribution equations

 

 

 

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