Moments and kurtosis

For a distribution, skewness is E[(X-μ)³]/σ³. Kurtosis β2=E[(X-μ)⁴]/σ⁴, and excess kurtosis=β2-3. Normal distributions have kurtosis 3 and excess 0. Values above or below 3 are called leptokurtic or platykurtic relative to the normal. Kurtosis concerns tail weight and extreme observations; peak height alone is an incomplete interpretation. Software may use bias-adjusted sample formulas, so record the convention.