Category:Factorial Moments

This category contains results about Factorial Moments.
Definitions specific to this category can be found in Definitions/Factorial Moments.

Let $X$ be a discrete random variable whose probability generating function is $\map {\Pi_X} s$.

The $n$th derivative of $\map {\Pi_X} s$ at $s = 1$:

$\dfrac {\d^n} {\d s^n} \map {\Pi_X} 1 = \expect {X \paren {X - 1} \cdots \paren {X - n + 1} }$

is called the $n$th factorial moment of $X$