NOTES ON KURTOSIS

 Definition of Kurtosis

Like skewness, kurtosis is a statistical measure that is used to describe the distribution.  Whereas skewness differentiates extreme values in one versus to other tail, kurtosis measures extreme values in either tail.  Distributions with large kurtosis exhibit tail data exceeding the tails of normal distribution.   Distribution with low kurtosis exhibit tail data that is generally less extreme than the tails of the normal distribution.  Kurtosis is a measure of the combined weight of a distributions tails relative to the center of the distribution.  When a set of approximately normal data is graphed via a histogram, it shows a bell peak and most data within + or –three standard deviations of the mean.  However, when high kurtosis is present, the tails extend farther than the + or – three standard deviations of the normal bell-curved distributions.  Kurtosis is 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 distribution can be infinitely peaked with low kurtosis, and a distribution can be perfectly flat-topped with infinite kurtosis.  Thus, kurtosis measures “tailedness”, not “peakedness”.

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 distribution has kurtosis statistic similar to that of the normal distribution, meaning that the extreme value characteristic of the distribution similar to that of a normal distribution.  The second category is leptokurtic distribution.  Any distribution that is leptokurtic displays greater kurtosis than a mesokurtic distribution. The final type of distribution is a platykurtic distribution. These types of distributions have short tails.

 

Figure 1.  Types of Kurtosis

Table 1

 Types of kurtosis and values

Sl No	Types of Kurtosis	Value
1	Mesokurtic	0.263
2	Leptokurtic	<0.263
3	Platykurtic	>0.263

Applications of kurtosis.

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 and may lead the researcher to choose alternative statistical methods.

POWER POINT ON KURTOSIS