Summary: The multinomial distribution.
Let n and r be positive integers and let
p1, . . . , pr
be such that
0 p 1 and
r
=1
p = 1.
Let
M(n, r)
be the set of r-tuples (n1, . . . , nr) of nonnegative integers such that
r
=1 = n. The discrete random vector
(N1, . . . , Nr) is said to have the r-nomial (multinomial in the book) distribution with parameters
n and p1, . . . , pr if
pN1,...,Nn (n1, . . . , nr) =
n
n1···nr
pn1
1 · · · pnr

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics