dist_hypergeometric: The Hypergeometric distribution

Description Usage Arguments Details See Also Examples

View source: R/dist_hypergeometric.R

Description

\lifecycle

stable

Usage

1

Arguments

m

The number of type I elements available.

n

The number of type II elements available.

k

The size of the sample taken.

Details

To understand the HyperGeometric distribution, consider a set of r objects, of which m are of the type I and n are of the type II. A sample with size k (k<r) with no replacement is randomly chosen. The number of observed type I elements observed in this sample is set to be our random variable X.

We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.

In the following, let X be a HyperGeometric random variable with success probability p = p = m/(m+n).

Support: x \in { \{\max{(0, k-n)}, …, \min{(k,m)}}\}

Mean: \frac{km}{n+m} = kp

Variance: \frac{km(n)(n+m-k)}{(n+m)^2 (n+m-1)} = kp(1-p)(1 - \frac{k-1}{m+n-1})

Probability mass function (p.m.f):

P(X = x) = \frac{{m \choose x}{n \choose k-x}}{{m+n \choose k}}

Cumulative distribution function (c.d.f):

P(X ≤ k) \approx Φ\Big(\frac{x - kp}{√{kp(1-p)}}\Big)

See Also

stats::Hypergeometric

Examples

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dist <- dist_hypergeometric(m = rep(500, 3), n = c(50, 60, 70), k = c(100, 200, 300))

dist
mean(dist)
variance(dist)
skewness(dist)
kurtosis(dist)

generate(dist, 10)

density(dist, 2)
density(dist, 2, log = TRUE)

cdf(dist, 4)

quantile(dist, 0.7)

distributional documentation built on Feb. 2, 2021, 5:09 p.m.