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

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

**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.