# What is the kurtosis of a negatively skewed distribution?

Feb 6, 2020

## What is the kurtosis of a negatively skewed distribution?

A distribution with a negative kurtosis value indicates that the distribution has lighter tails than the normal distribution. For example, data that follow a beta distribution with first and second shape parameters equal to 2 have a negative kurtosis value.

## What does it mean when your kurtosis is negative?

Negative values of kurtosis indicate that a distribution is flat and has thin tails. Platykurtic distributions have negative kurtosis values. A platykurtic distribution is flatter (less peaked) when compared with the normal distribution, with fewer values in its shorter (i.e. lighter and thinner) tails.

What does negative skewness and kurtosis mean?

That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers. Negative values for the skewness indicate data that are skewed left and positive values for the skewness indicate data that are skewed right.

Can skewness and kurtosis be negative?

In statistics, kurtosis is used to describe the shape of a probability distribution. Specifically, it tells us the degree to which data values cluster in the tails or the peak of a distribution. The kurtosis for a distribution can be negative, equal to zero, or positive.

### How do you interpret kurtosis and skewness?

For skewness, if the value is greater than + 1.0, the distribution is right skewed. If the value is less than -1.0, the distribution is left skewed. For kurtosis, if the value is greater than + 1.0, the distribution is leptokurtik. If the value is less than -1.0, the distribution is platykurtik.

A low or negative kurtosis means that on a period-by-period basis most observations fall within a predictable band. The risk that does occur happens within a moderate range, and there is little risk in the tails.

What should skewness and kurtosis be?

The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). (2010) and Bryne (2010) argued that data is considered to be normal if skewness is between ‐2 to +2 and kurtosis is between ‐7 to +7.

A negative skew is generally not good, because it highlights the risk of left tail events or what are sometimes referred to as “black swan events.” While a consistent and steady track record with a positive mean would be a great thing, if the track record has a negative skew then you should proceed with caution.

## How does skewness and kurtosis affect your distribution?

Skewness is the extent to which the data are not symmetrical. Whether the skewness value is 0, positive, or negative reveals information about the shape of the data. As data becomes more symmetrical, its skewness value approaches zero. Figure A shows normally distributed data, which by definition exhibits relatively little skewness.

## What is the meaning of negative coefficient of kurtosis?

A distribution with a negative kurtosis value indicates that the distribution has lighter tails than the normal distribution. For example, data that follow a beta distribution with first and second shape parameters equal to 2 have a negative kurtosis value.

What is the difference between positive and negative skewness?

Perfectly symmetrical data would have a skewness value of 0. A negative skewness value implies that a distribution has its tail on the left side of the distribution, while a positive skewness value has its tail on the on the right side of the distribution. Positive skew and negative skew

How is the shape of a probability distribution related to kurtosis?

Like skewness, kurtosis describes the shape of a probability distribution and there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Different measures of kurtosis may have different interpretations .