Statistics – Kurtosis:

Kurtosis is a measure of thickness of a variable distribution found in the tails. The outliers in the given data have more effect on this measure. Moreover, it does not have any unit. The kurtosis of a distribution can be classified as leptokurtic, mesokurtic and platykurtic.

Leptokurtic distributions are variable distributions with wide and heavier tails and have positive kurtosis(kurtosis >0). As the name tells us lepto means slender. Examples of leptokurtic distributions are Student’s t-distribution, Rayleigh distribution, Laplace distribution, exponential distribution, Poisson distribution and the logistic distribution.

Platykurtic distributions have narrow and lighter tails and thus have negative kurtosis(kurtosis <0). As the name tells us platy means broad. Examples of platykurtic distributions are continuous or discrete uniform distributions, the raised cosine distribution, the Bernoulli distribution.

Mesokurtic distributions (such as the normal distribution) have a kurtosis of zero. Most often, kurtosis is measured against the normal distribution. For example, the binomial distribution is mesokurtic.

Diagrammatically, shows the shape of three different types of curves.

The normal curve is called Mesokurtic curve. If the curve of a distribution is more peaked than a normal or mesokurtic curve then it is referred to as a Leptokurtic curve. If a curve is less peaked than a normal curve, it is called as a platykurtic curve.

Formula :

The sample kurtosis is a useful measure of whether there is a problem with outliers in a data set. Larger kurtosis indicates a more serious outlier problem, which helps researcher to choose alternative statistical methods.