au.id.cxd.math.probability.discrete
HyperGeometric
Related Docs:
object HyperGeometric
| package discrete
au.id.cxd.math.probability.discrete
cumulative distribution function
cumulative distribution function
mean $\mu$ of the distribution
mean $\mu$ of the distribution
calculate the probability of selecting y (select Size) samples
calculate the probability of selecting y (select Size) samples
standard deviation $\sigma$
standard deviation $\sigma$
variance for the distribution $\sigma^2$
variance for the distribution $\sigma^2$
Created by cd on 7/09/2014.
Hyper geometric
The Hypergeometric (class name HyperGeometric) distribution represents the probability of choosing $y$ number of events of the same kind from a subset of $r$ like items within a population of all $N$ possible items (of different kinds) for the sample of size $n$ containing the mixed items.
The constraints are such that $r \le n \le N$ and $y \le r \le n$. The parameters are $y,r,n,N$.
The probability distribution is defined as follows. $$ P(y; r,n,N) = \frac{ {r \choose y } {{N - r} \choose {n - y} } } { {N \choose n} } $$
The simple properties of the distribution are:\\\\ Mean: $\mu = \frac{nr}{N}$\\ Variance: $\sigma^2 = n \left( \frac{r}{N} \right) \left( \frac{N - r}{N} \right) \left( \frac{N - n}{N-1}\right)$
r <= n <= N y <= r <= n