Kurtosis is a statistical method that measures Tailedness i.e. how often outliers occur. It is the measure of how much the tails of distribution vary relative to the tails of a Normal Distribution.
- A positive value of Kurtosis means heavy tails (a lot of data in tails).
- A negative value of Kurtosis means light tails (little data in tails).
In the case of Normal Distribution, 99.7% of data is present within 3 standard deviations from the center. The Data present beyond the 3 standard deviations is considered to be an outlier. When high kurtosis is present, the tails extend farther than the three standard deviations of the normal bell-curved distribution. Hence the kurtosis of a normal distribution equals 3.
Excess kurtosis is a measure of the kurtosis of distribution against the kurtosis of a normal distribution.
Excess Kurtosis = Kurtosis - 3
- Excess kurtosis for the normal distribution is 0 (i.e. 3 -3 = 0).
- Negative Excess kurtosis means lighter tails (flatter) than a normal distribution.
- Positive Excess kurtosis means heavier tails than a normal distribution.
Types of Kurtosis
Kurtosis is categorized into 3 categories based on the value of Excess Kurtosis.
- Mesokurtic Kurtosis
- Leptokurtic Kurtosis
- Platykurtic Kurtosis
- Excess Kurtosis is 0 or close to 0.
- It follows Normal Distribution.
- Excess Kurtosis is positive i.e. greater than Mesokurtic Kurtosis.
- It has heavy tails (a lot of data in tails) which indicate high outliers.
- The peak is thin.
- Excess Kurtosis is negative i.e. lower than Mesokurtic Kurtosis.
- It has flatter tails (little data in tails) which indicate small outliers.
- The peak is short and flat.
Applications of Kurtosis
Kurtosis has application in financial risk analysis. High Kurtosis means investment is risky whereas a small kurtosis means a low or moderate level of risk.