Erl {Distributacalcul}

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 + 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 N total items of which m are of one type and n of the other and from which k items are picked has probability mass function :

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

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

Value

Function :

• expValErl gives the expected value.

• varErl gives the variance.

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)