Kurtosis is the statistical measure that tells us when a distribution is more or less peaked tahn a normal distribution.

Different formulae for measuring kurtosis are:

i) Moment coefficient of kurtosis

One measure of kurtosis uses the fourth moment about the mean expresses in dimensionless form:

which is often denoted as b₂

ii) Excess kurtosis:

Kurtosis is more commonly defined as the fourth cumulant divided by the square of the second cumulant, which is equal to the fourth moment around the mean divided by the square of the variance minus 3,

• means leptokurtic distribution.
• means mesokurtic distribution.
•  means platikurtic distribution.

iii) Percentile coefficient of kurtosis

Another measure of kurtosis is based on both quartiles and percentiles and is given by:

where is the semi-interquartile range.