Definition
Suppose X is an n × p matrix, each row of which is independently drawn from a p-variate normal distribution with zero mean:
Then the Wishart distribution is the probability distribution of the p×p random matrix
known as the scatter matrix. One indicates that S has that probability distribution by writing
The positive integer n is the number of degrees of freedom. Sometimes this is written W(V, p, n). For n ≥ p the matrix S is invertible with probability 1 if V is invertible.
If p = 1 and V = 1 then this distribution is a chi-squared distribution with n degrees of freedom.
Read more about this topic: Wishart Distribution
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)