Erl {Distributacalcul}R Documentation

Hypergeometric Distribution

Description

Hypergeometric distribution where we have a sample of k balls from an urn containing N, of which m are white and n are black.

Usage

expValErl(N = n + m, m, n = N - m, k)

varErl(N = n + m, m, n = N - m, k)

Arguments

N

Total number of balls (white and black) in the urn. N=n+mN = n + m

m

Number of white balls in the urn.

n

Number of black balls in the urn. Can specify n instead of N.

k

Number of balls drawn from the urn, k = 0, 1, ..., m + n.

Details

The Hypergeometric distribution for NN total items of which mm are of one type and nn of the other and from which kk items are picked has probability mass function :

Pr(X=x)=(mk)(nkx)(Nk)Pr(X = x) = \frac{\left(\frac{m}{k}\right)\left(\frac{n}{k - x}\right)}{\left(\frac{N}{k}\right)}

for x=0,1,,min(k,m)x = 0, 1, \dots, \min(k, m).

Value

Function :

Invalid parameter values will return an error detailing which parameter is problematic.

Examples


# With total balls specified
expValErl(N = 5, m = 2, k = 2)

# With number of each colour of balls specified
expValErl(m = 2, n = 3, k = 2)


# With total balls specified
varErl(N = 5, m = 2, k = 2)

# With number of each colour of balls specified
varErl(m = 2, n = 3, k = 2)


[Package Distributacalcul version 0.4.0 Index]