Kurtosis

Kurtosis is a measure of the peakedness of the distribution of a real-valued random variable. A normal distribtution has a kurtosis of zero (distributions with this kurtosis are called mesokurtic). A distribution with positive kurtosis is called leptokurtic, and one with negative kurtosis platykurtic.

Kurtosis is defined as μ₄ / σ⁴ − 3, where μ₄ is the fourth moment about the mean and σ is the standard deviation.

For a set of N values the kurtosis can be calculated as Σ_i(x_i - μ)⁴ / Nσ⁴ − 3, where x_i is the i^th value and μ is the mean.