The th cumulant is the coefficient of in the cumulant-generating function. The first two cumulants are the expected value and variance; the third is the third central moment.
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Cumulants are a set of statistical measures that provide insights into the shape and characteristics of a probability distribution. They are particularly useful in the context of higher-order moments and can be seen as an alternative to moments. While moments (like the mean, variance, skewness, and kurtosis) capture information about a distribution, cumulants provide a different perspective that can simplify certain types of statistical analysis.