mesokurtic

Mesokurtic describes a statistical distribution whose kurtosis, a measure of peakedness and tail heaviness, is similar to that of the normal distribution. In most conventions, this means the excess kurtosis is approximately zero or the kurtosis is close to 3. A mesokurtic distribution thus has a moderate peak and tails that are neither particularly heavy nor particularly light compared with the normal distribution.

Kurtosis summarizes tail behavior and the sharpness of the distribution’s peak. When a distribution is mesokurtic, its tail heaviness and central peak resemble those of the normal distribution. This makes it a reference point in many statistical analyses, where departures from mesokurticity indicate deviations from normality in terms of tails or peak.

Classification contrast: leptokurtic and platykurtic. Leptokurtic distributions have a sharper peak and fatter tails (positive excess kurtosis), indicating more outliers than the normal model. Platykurtic distributions have a flatter peak and thinner tails (negative excess kurtosis). Mesokurtic sits between these extremes, reflecting a more “normal-like” shape.

Examples and notes. The normal distribution is the canonical mesokurtic example. The uniform distribution is platykurtic due to its flat peak and bounded tails. The Laplace distribution is leptokurtic with a very sharp peak and heavy tails in comparison to normal. Some t-distributions with sufficiently large degrees of freedom have kurtosis near mesokurtic values. Caution is warranted with distributions that have infinite variance, such as the Cauchy, where kurtosis is undefined. In practice, kurtosis is sensitive to outliers and finite-sample estimation can be unstable.