# Which kurtosis has fat tails?

## Which kurtosis has fat tails?

Leptokurtic distributions are statistical distributions with kurtosis greater than three. It can be described as having a wider or flatter shape with fatter tails resulting in a greater chance of extreme positive or negative events.

## How do you calculate kurtosis?

Kurtosis = Fourth Moment / Second Moment2

1. Kurtosis = 313209 / (365)2
2. Kurtosis = 2.35.

Does high kurtosis mean fat tails?

Excess kurtosis. Kurtosis measures the “fatness” of the tails of a distribution. Positive excess kurtosis means that distribution has fatter tails than a normal distribution. Fat tails means there is a higher than normal probability of big positive and negative returns realizations.

### How do you determine if a distribution is heavy-tailed?

A heavy tailed distribution has a tail that’s heavier than an exponential distribution (Bryson, 1974). In other words, a distribution that is heavy tailed goes to zero slower than one with exponential tails; there will be more bulk under the curve of the PDF.

### Which distribution has fatter tails?

A leptokurtic distribution has excess positive kurtosis. The tails are “fatter” than the normal distribution, hence the term fat-tailed.

How do you find the kurtosis of a normal distribution?

The normal distribution has skewness equal to zero. The kurtosis of a probability distribution of a random variable x is defined as the ratio of the fourth moment μ4 to the square of the variance σ4, i.e., μ 4 σ 4 = E { ( x − E { x } σ ) 4 } E { x − E { x } } 4 σ 4 . κ = μ 4 σ 4 −3 .

## Why is high kurtosis bad?

The risk that does occur happens within a moderate range, and there is little risk in the tails. Alternatively, the higher the kurtosis, the more it indicates that the overall risk of an investment is driven by a few extreme “surprises” in the tails of the distribution.

## What causes fat tail distribution?

By definition, a fat tail is a probability distribution which predicts movements of three or more standard deviations more frequently than a normal distribution. Even before the financial crisis, periods of financial stress had resulted in market conditions represented by fatter tails.

What is the kurtosis of a normal distribution?

A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. An increased kurtosis (>3) can be visualized as a thin “bell” with a high peak whereas a decreased kurtosis corresponds to a broadening of the peak and “thickening” of the tails.

### What is kurtosis or fat tails?

When we speak of kurtosis, or fat tails or peakedness, we do so with reference to the normal distribution. We compare other distributions to the normal distribution, so it is important to be clear about the shape of the normal distribution. So let us spend a few minutes talking about the shape of the normal distribution.

### What is the kurtosis formula in statistics?

What is the Kurtosis Formula? The term “Kurtosis” refers to the statistical measure that describes the shape of either tail of a distribution, i.e. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution.

Which distribution has a large kurtosis?

A heavy-tailed distribution has large kurtosis. The canonical distribution that has a large positive kurtosis is the t distribution with a small number of degrees of freedom. Some heavy-tailed distributions have infinite kurtosis.

## What are the tails of a distribution curve?

The tails of a distribution measure the number of events that occurred outside of the normal range. Unlike skewness, kurtosis measures either tail’s extreme values. Excess kurtosis means the distribution of event outcomes have lots of instances of outlier results, causing fat tails on the bell-shaped distribution curve .

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