Kurtosis - Terminology and Examples

Terminology and Examples

A high kurtosis distribution has a sharper peak and longer, fatter tails, while a low kurtosis distribution has a more rounded peak and shorter, thinner tails.

Distributions with zero excess kurtosis are called mesokurtic, or mesokurtotic. The most prominent example of a mesokurtic distribution is the normal distribution family, regardless of the values of its parameters. A few other well-known distributions can be mesokurtic, depending on parameter values: for example the binomial distribution is mesokurtic for .

A distribution with positive excess kurtosis is called leptokurtic, or leptokurtotic. "Lepto-" means "slender". In terms of shape, a leptokurtic distribution has a more acute peak around the mean and fatter tails. Examples of leptokurtic distributions include the Cauchy distribution, Student's t-distribution, Rayleigh distribution, Laplace distribution, exponential distribution, Poisson distribution and the logistic distribution. Such distributions are sometimes termed super Gaussian.

A distribution with negative excess kurtosis is called platykurtic, or platykurtotic. "Platy-" means "broad". In terms of shape, a platykurtic distribution has a lower, wider peak around the mean and thinner tails. Examples of platykurtic distributions include the continuous or discrete uniform distributions, and the raised cosine distribution. The most platykurtic distribution of all is the Bernoulli distribution with p = ½ (for example the number of times one obtains "heads" when flipping a coin once, a coin toss), for which the excess kurtosis is −2. Such distributions are sometimes termed sub Gaussian.