# Kurtosis

## A Simple Explanation - By Varsha Saini

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.

• 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

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.

1. Mesokurtic Kurtosis
2. Leptokurtic Kurtosis
3. Platykurtic Kurtosis

Mesokurtic Kurtosis

• Excess Kurtosis is 0 or close to 0.
• It follows Normal Distribution.

Leptokurtic Kurtosis

• 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.

Platykurtic Kurtosis

• 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.