Kurtosis

Kurtosis is a statistical measure that describes the shape of a probability distribution. It quantifies the extent to which a distribution deviates from the shape of the normal distribution, also known as the Gaussian distribution or the bell curve.

Types of Kurtosis

There are three types of kurtosis:

  1. Leptokurtic: A leptokurtic distribution has positive kurtosis and is characterized by a relatively high peak and heavy tails compared to the normal distribution. The data in this distribution has more outliers and extreme values.
  2. Mesokurtic: A mesokurtic distribution has kurtosis equal to zero, indicating that it follows a perfectly normal distribution.
  3. Platykurtic: A platykurtic distribution has negative kurtosis and is characterized by a relatively flat or spread-out shape compared to the normal distribution. The data in this distribution has fewer outliers and extreme values.

Kurtosis Calculation

The kurtosis of a dataset can be calculated using various formulas, but the most commonly used formula is based on the fourth moment of the data. This formula subtracts 3 from the sample kurtosis to make the kurtosis of a normal distribution equal to zero.

Interpreting Kurtosis

Kurtosis provides insights into the peakedness or flatness of a distribution and the presence of outliers or extreme values. However, it does not capture the direction of the outliers (whether they are high or low values).

A kurtosis value of:

  • Greater than 3 indicates leptokurtic distribution.
  • Equal to 3 indicates a perfectly normal distribution (mesokurtic).
  • Less than 3 indicates platykurtic distribution.

It is important to interpret kurtosis in conjunction with other statistical measures to gain a comprehensive understanding of the data distribution.