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Download a pdf copy of this help file here |
Format: VoseBetaGeometric(a, b, U)
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 BetaGeometric distribution has the same relationship to the
BetaBinomial distribution
as the Geometric distribution
is to the Binomial.
Example:
Imagine that you have taken a random sample of size n from a population. From order statistics theory, the position of the smallest of these values falls on the cumulative distribution of the population F(x) at Beta(1,n). Thus, the size of a new sample you will need to take (assuming the population is much larger than the sample size) to see a new value lower than the current minimum is:
1+BetaGeometric(1,n)
The BetaGeometric models the failures (the values are > current minimum) and the ‘1’ models the final success.
By reflection, the same formula models how many individuals you’ll need to randomly sample before observing a value greater than the current maximum.
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 by . (equations)
Zero-truncated model - we entirely remove the probability of zero events occurring. (equations)
See also: Zero-modified counting distributions
VoseBetaGeometric generates values from this distribution or calculates a percentile
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
