# Link between cumulants and kurtosis

Hey in "Financial modelling with Jump processes" by Cont and Tankov is written that kurtosis of distribution of random variable $$X$$ is equal to $$\frac{c_4(X)}{c_2(X)^2}$$ where $$c_n$$ denotes $$n$$-th cumulant of $$X$$. But for normal distribution $$c_4=0$$ so kurtosis should be $$0$$ but it is equal $$3$$. So there shouldn't be that $$s(X)=3+\frac{c_4(X)}{c_2(X)^2}$$?

• Yes, technically excess kurtosis is the fourth cumulant divided by the square of the second cumulant. The author left out the word "excess" but he is clearly using that definition, just adjust your thinking accordingly., even if you prefer the other definition, the one that includes the 3. – noob2 Sep 29 at 13:21