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:
“The probability of learning something unusual from a newspaper is far greater than that of experiencing it; in other words, it is in the realm of the abstract that the more important things happen in these times, and it is the unimportant that happens in real life.”
—Robert Musil (18801942)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (18791955)