In Probability Theory
In probability theory Mellin transform is an essential tool in studying the distributions of products of random variables. If X is a random variable, and X+ = max{X,0} denotes its positive part, while X − = max{−X,0} is its negative part, then the Mellin transform of X is defined as
where γ is a formal indeterminate with γ2 = 1. This transform exists for all s in some complex strip D = {s: a ≤ Re(s) ≤ b}, where a ≤ 0 ≤ b.
The Mellin transform of a random variable X uniquely determines its distribution function FX. The importance of the Mellin transform in probability theory lies in the fact that if X and Y are two independent random variables, then the Mellin transform of their products is equal to the product of the Mellin transforms of X and Y:
Read more about this topic: Mellin Transform
Famous quotes containing the words probability and/or theory:
“Only in Britain could it be thought a defect to be too clever by half. The probability is that too many people are too stupid by three-quarters.”
—John Major (b. 1943)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes So much the worse for the facts: let them be altered, instead of So much the worse for my theory.”
—George Bernard Shaw (18561950)