Distribution to estimate a sub-population size from hypergeometric sampling


Format: HypergeoD(s, n, M)


A HypergeoD(s, n, M) is a discrete bounded distribution used to estimate the size of a sub-population D in a Hypergeometric process.


The HypergeoD distribution models the size of a sub-population D when one knows the population size M, the size of a random sample taken n, and the number in that sample that were from the sub-population s.

Since we have already observed s from this sub-population, and since (n-s)  were not from the sub-population, the HypergeoD is bounded on [s, M-(n-s)].


There are four parameters for a Hypergeometric process: s, n, D, M. Knowing any three allows us to construct a distribution to estimate the fourth – see Hypergeometric process.

ModelRisk functions added to Microsoft Excel for the Hypergeometric-D distribution

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

VoseHypergeoDObject constructs a distribution object for this distribution.

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

VoseHypergeoDProb10 returns the log10 of the probability mass or cumulative distribution function.


HyperpgeoD distribution equations



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