Kurtosis is a characteristic used in probability to measure the peakedness of a probability distribution. This measure represents a way of describing a data set which should be normally distributed. This concept of kurtosis is one which helps to describe the shape of a probability distribution, which under the normal distribution should take on a bell-shaped curve. The measure of kurtosis indicates whether the distribution is flat, highly peaked or normal.
There are specific terms which are used in statistics to describe the kurtosis of a distribution. The term platykurtic is used to when the distribution is flat, leptokurtic describes when the distribution is peaked and mesokurtic describes a normal distribution (1). In terms of visual appearance, a platykurtic distribution is one in which the peak is very pointed and tall and the tails are thick. On the other hand, a leptokurtic distribution has very thin tails and a very flat, broad peak. Of course, a mesokurtic distribution is representative of a nice bell-shaped curve.
Evaluating the shape of the curve is qualitative in nature and thus, the problem of subjectivity can arise. Therefore, to counter this problem, there is also a numerical way to determine the kurtosis value associated with a distribution. Kurtosis is known to be the fourth value around the mean and can be evaluated using the following formula (2):
β2 = E(x – μ)4 /σ4
β2 = kurtosis
μ = mean
σ = standard deviation
x = random variable