Platykurtosis

Platykurtosis refers to a statistical property of a probability distribution where the distribution has a lower, flatter peak and thinner tails than the normal distribution. It corresponds to negative excess kurtosis, meaning the kurtosis value is less than 3 (or, equivalently, the excess kurtosis is negative). In practical terms, data with platykurtic shape tend to have fewer extreme outliers relative to a normal distribution.

A platykurtic distribution spreads probability more evenly across its range. The central peak is less pronounced and the tails are lighter, giving a flatter appearance on a histogram or density plot. This contrasts with leptokurtosis, which exhibits a sharp peak and heavier tails, and mesokurtosis, which closely resembles the normal distribution in kurtosis.

Canonical examples include the uniform distribution on an interval, which is notably platykurtic with negative excess kurtosis. Other distributions can be platykurtic for certain parameter choices, including some beta distributions and certain mixtures. Whether a distribution is platykurtic depends on its shape and tail behavior rather than on variance alone.

Interpretation and cautions: Kurtosis estimates are sensitive to sample size and outliers, and finite samples can produce unstable measures of platykurtosis. As with other moments, platykurtosis should be considered alongside measures of central tendency, dispersion, and skewness, and often supported by visual inspection of the data distribution.