Kurtosis

DEFINITION of 'Kurtosis'

Kurtosis is a statistical measure that's used to describe the distribution, or skewness, of observed data around the mean, sometimes referred to as the volatility of volatility. Kurtosis is used generally in the statistical field to describes trends in charts. Kurtosis can be present in a chart with fat tails and a low, even distribution, as well as be present in a chart with skinny tails and a distribution concentrated toward the mean.

BREAKING DOWN 'Kurtosis'

Put simply, kurtosis is a measure of the combined weight of a distribution's tails relative to the rest of the distribution. When a set of data is graphically depicted, it usually has a standard normal distribution, like a bell curve, with a central peak and thin tails. However, when kurtosis is present, the tails of the distribution are different than they would be under a normal bell-curved distribution.

Kurtosis is sometimes confused with a measure of the peakedness of a distribution. However, kurtosis is a measure that describes the shape of a distribution's tails in relation to its overall shape. A data set that shows kurtosis sometimes also displays skewness, or a lack of symmetry. However, kurtosis can be evenly distributed so that both its tails are equal.

Types of Kurtosis

There are three categories of kurtosis that can be displayed by a set of data. All measures of kurtosis are compared against a standard normal distribution, or bell curve.

The first category of kurtosis is a mesokurtic distribution. This type of kurtosis is the most similar to a standard normal distribution in that it also resembles a bell curve. However, a graph that is mesokurtic has fatter tails than a standard normal distribution and has a slightly lower peak. This type of kurtosis is considered normally distributed but is not a standard normal distribution.

The second category is a leptokurtic distribution. Any distribution that is leptokurtic displays greater kurtosis than a mesokurtic distribution. Characteristics of this type of distribution is one with extremely thick tails and a very thin and tall peak. The prefix of "lepto-" means "skinny," making the shape of a leptokurtic distribution easier to remember. T-distributions are leptokurtic.

The final type of distribution is a platykurtic distribution. These type of distributions have slender tails and a peak that's smaller than a mesokurtic distribution. The prefix of "platy-" means "broad," and it is meant to describe a short and broad-looking peak. Uniform distributions are platykurtic.

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