Wishart Distribution - Definition

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 np 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:

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.
    Ralph Waldo Emerson (1803–1882)

    Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?
    Richard Eberhart (b. 1904)