View source: R/dist_hypergeometric.R
dist_hypergeometric | R Documentation |
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
.
dist_hypergeometric(m, n, k)
m |
The number of type I elements available. |
n |
The number of type II elements available. |
k |
The size of the sample taken. |
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)}, \dots, \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 \le k) \approx \Phi\Big(\frac{x - kp}{\sqrt{kp(1-p)}}\Big)
stats::Hypergeometric
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)
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