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 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.

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.

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 is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers.

The general guideline for the interpretation of kurtosis is that if the number is greater than +1, then the distribution is too peaked. But if kurtosis' number is less than –1, it shows a flat distribution. Distributions exhibiting skewness and/or kurtosis that exceed these guidelines are considered non-normal." (Hair et al., 2017, p.

If the kurtosis is greater than 3, then the data set is said to have heavier tails than a normal distribution. When the kurtosis is less than 3, then the data set is interpreted to be more light-tailed than a normal distribution.

Both skew and kurtosis can be interpreted through descriptive statistics. Acceptable values of skewness fall between − 3 and + 3, and kurtosis is appropriate from a range of − 10 to + 10 when using SEM (Brown, 2006).

The kurtosis of any univariate normal distribution is 3. It is therefore usual to contrast the kurtosis of a distribution to this value. Distributions whose kurtosis value is less than 3 are called platykurtic, although, this does not automatically mean that the distribution is "flat-topped" as is sometimes stated.

Kurtosis is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers. There are three types of kurtosis; mesokurtic, leptokurtic, and platykurtic.

Kurtosis is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers.

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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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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The general guideline for the interpretation of kurtosis is that if the number is greater than +1, then the distribution is too peaked. But if kurtosis' number is less than –1, it shows a flat distribution.
Distributions exhibiting skewness and/or kurtosis that exceed these guidelines are considered non-normal." (Hair et al., 2017, p.

If the kurtosis is greater than 3, then the data set is said to have heavier tails than a normal distribution. When the kurtosis is less than 3, then the data set is interpreted to be more light-tailed than a normal distribution.

Both skew and kurtosis can be interpreted through descriptive statistics. Acceptable values of skewness fall between − 3 and + 3, and kurtosis is appropriate from a range of − 10 to + 10 when using SEM (Brown, 2006).

The kurtosis of any univariate normal distribution is 3. It is therefore usual to contrast the kurtosis of a distribution to this value. Distributions whose kurtosis value is less than 3 are called platykurtic, although, this does not automatically mean that the distribution is "flat-topped" as is sometimes stated.

Kurtosis is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers. There are three types of kurtosis; mesokurtic, leptokurtic, and platykurtic.