# BetaGeometric distribution

Format: BetaGeometric(a, b)

## Uses

The BetaGeometric(a, b) distribution models the number of failures that will occur in a binomial process before the first success is observed and where the binomial probability p is itself a random variable taking a Beta(a, b) distribution.

Thus the Beta Geometric distribution has the same relationship to the Beta Binomial distribution as the Geometric distribution is 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 events.

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

## ModelRisk functions added to Microsoft Excel for the Beta-Geometric distribution

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

VoseBetaGeometricObject constructs a distribution object for this distribution.

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

VoseBetaGeometricProb10 returns the log10 of the probability mass or cumulative distribution function.

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

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

VoseBetaGeometricFitP returns the parameters of this distribution fitted to data.

## ModelRisk functions added to Microsoft Excel for the Zero-Inflated Beta-Geometric distribution

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

VoseZIBetaGeometricObject constructs a distribution object for this distribution.

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

VoseZIBetaGeometricProb10 returns the log10 of the probability mass or cumulative distribution function.

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

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

VoseZIBetaGeometricFitP returns the parameters of this distribution fitted to data.

## ModelRisk functions added to Microsoft Excel for the Zero-Truncated Beta-Geometric distribution

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

VoseZTBetaGeometricObject constructs a distribution object for this distribution.

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

VoseZTBetaGeometricProb10 returns the log10 of the probability mass or cumulative distribution function.

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

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

VoseZTBetaGeometricFitP returns the parameters of this distribution fitted to data.