How is kurtosis of a distribution calculated in R
While skew measures if the distribution is left skewed or right skewed, kurtosis measures if the tail is thin or thick.
A tail is thick if the standard distribution is large. For example,
> p_kurtosis = data.frame(v=rnorm(1000,mean=100,sd=50))
Similarly, if the sd is small ( more tightly packed around the center ), the tail is thin.
> n_kurtosis = data.frame(v=rnorm(1000,mean=100,sd=10))
Let’s visualize this.
ggplot() + geom_density(data = p_kurtosis,aes(p_kurtosis,fill="red",alpha=0.1)) + geom_density(data = n_kurtosis, aes(n_kurtosis,fill="green",alpha=0.1))
The distribution in green has a thick tail , hence a positive kurtosis. The distribution in red has a relatively think tail and hence a negative kurtosis.
> kurtosis(p_kurtosis$v)  0.1529404 > kurtosis(n_kurtosis$v)  -0.01435051
skewness and kurtosis are a bit related. Learn more about how to measure skewness of a distribution in R here.