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Format: VoseInvHypergeo(s, D, M,
U)
Inverse Hypergeometric equations
The Inverse Hypergeometric distribution InvHypergeo(s,D,M) models the number of failures one would have before achieving the sth success in a hypergeometric sampling where there are D individuals of interest (their selection is a 'success') in a population of size M. Four examples of the Inverse Hypergeometric distribution are shown below:
It should be used in any situation where there is Hypergeometric sampling and one is asking the question: "How many failures will I observe before I get s successes?", or alternatively "How many samples do I need to s successes?".
Imagine that a credit card company estimates that 20 of its 450 platinum card holders have gained their wealth illegally. A banking regulator is to perform an audit. How many randomly selected platinum card holders will they have to investigate before finding a criminal? Answer: InvHypergeo(1,20,450) + 1.
The Inverse Hypergeometric goes by a variety of other names: negative hypergeometric distribution, hypergeometric waiting time distribution, and the Markov-Polya distribution.
The complexity of constructing the Inverse hypergeometric distribution makes it an appealing candidate to be approximated. Where the Hypergeometric process is closely approximated by a Binomial process (roughly, where the sample size is less than 10% of the population size), the Inverse Hypergeometric distribution is approximated by a Negative Binomial. Similarly, where D/M is small, the Inverse Hypergeometric distribution is approximated by the Gamma.
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
VoseInvHypergeo generates values from this distribution or calculates a percentile
VoseInvHypergeoObject constructs a distribution object for this distribution
VoseInvHypergeoProb returns the probability mass or cumulative distribution function for this distribution
VoseInvHypergeoProb10 returns the log10 of the probability mass or cumulative distribution function
VoseInvHyperGeoFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution
VoseInvHyperGeoFitObject constructs a distribution object of this distribution fitted to data
VoseInvHyperGeoFitFitP returns the parameters of this distribution fitted to data
