The cumulant generating function (CGF) is a mathematical tool used in probability theory and statistics that provides a way to summarize the properties of a probability distribution. It is defined as the logarithm of the moment generating function (MGF), and it serves to compute the cumulants of a distribution, which are essential for understanding its shape and behavior. The CGF allows for a convenient way to derive relationships between different moments of the distribution, making it a powerful concept in the study of random variables.
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