Cumulant

Summary

The cumulants $\kappa_1, \kappa_2, \dots$ of a real random variable are the Taylor coefficients at $0$ of its cumulant generating function, the logarithm of the moment-generating function. The first cumulant is the mean and the second is the variance. Cumulants of a sum of independent random variables are the sums of their cumulants, which makes them easier to use than moments. The normal distribution is the law whose cumulants of order $3$ and higher all vanish.