Factorial moment generating function

In probability theory and statistics, the factorial moment generating function of the probability distribution of a real-valued random variable X is defined as

for all complex numbers t for which this expected value exists. This is the case at least for all t on the unit circle $|t|=1$ , see characteristic function. If X is a discrete random variable taking values only in the set {0,1, ...} of non-negative integers, then $M_X$ is also called probability-generating function of X and $M_X(t)$ is well-defined at least for all t on the closed unit disk $|t|\le1$ .

单词	Factorial moment generating function
释义	Factorial moment generating function 英语百科 Factorial moment generating function In probability theory and statistics, the factorial moment generating function of the probability distribution of a real-valued random variable X is defined as for all complex numbers t for which this expected value exists. This is the case at least for all t on the unit circle $\|t\|=1$ , see characteristic function. If X is a discrete random variable taking values only in the set {0,1, ...} of non-negative integers, then $M_X$ is also called probability-generating function of X and $M_X(t)$ is well-defined at least for all t on the closed unit disk $\|t\|\le1$ .
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