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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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更新时间:2025/6/20 12:18:42