## Kurtosis

## Definition

In probability theory and statistics, kurtosis is a measure of the "tailedness" of the probability distribution of a real-valued random variable. In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Depending on the particular measure of kurtosis that is used, there are various interpretations of kurtosis, and of how particular measures should be interpreted.

### Kurtosis

### What is 'Kurtosis'

Kurtosis is a statistical measure that's used to describe the distribution, or skewness, of observed data around the mean, sometimes referred to as the volatility of volatility. Kurtosis is used generally in the statistical field to describes trends in charts. Kurtosis can be present in a chart with fat tails and a low, even distribution, as well as be present in a chart with skinny tails and a distribution concentrated toward the mean.

### Explaining 'Kurtosis'

Put simply, kurtosis is a measure of the combined weight of a distribution's tails relative to the rest of the distribution. When a set of data is graphically depicted, it usually has a standard normal distribution, like a bell curve, with a central peak and thin tails. However, when kurtosis is present, the tails of the distribution are different than they would be under a normal bell-curved distribution.

### Types of Kurtosis

There are three categories of kurtosis that can be displayed by a set of data. All measures of kurtosis are compared against a standard normal distribution, or bell curve.

### Kurtosis FAQ

#### What kurtosis tells us?

#### How do you interpret kurtosis?

#### What does a kurtosis of 3 mean?

#### What is the normal range for kurtosis?

#### What is normal kurtosis?

#### What is kurtosis in statistics with example?

#### What is a kurtosis in statistics?

### Further Reading

**Autoregresive conditional volatility, skewness and kurtosis**

www.sciencedirect.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Autoregressive conditional kurtosis**

academic.oup.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Modeling asymmetry and excess kurtosis in stock return data**

papers.ssrn.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Co‐kurtosis and capital asset pricing**

onlinelibrary.wiley.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Persistence and kurtosis in GARCH and stochastic volatility models**

academic.oup.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Kurtosis of GARCH and stochastic volatility models with non-normal innovations**

www.sciencedirect.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**A note on skewness and kurtosis adjusted option pricing models under the Martingale restriction**

www.tandfonline.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements**

www.sciencedirect.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Do investors dislike kurtosis?**

papers.ssrn.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

**Kurtosis as Peakedness, 1905–2014.**

www.tandfonline.com [PDF]

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …