# Kurtosis

## Definition of Kurtosis

Kurtosis: A measure of the peakedness or flatness of a distribution, Kurtosis is determined by calculating the fourth moment of the distribution about its mean. Distributions with high kurtosis are more peaked than those with low kurtosis, while distributions with low kurtosis are more spread out.

## How is Kurtosis used?

Kurtosis is a statistical measure used to describe the shape of the probability distribution of a given data set. It is used to compare the ‘peakedness’ of a distribution – that is, how extreme or sharp its central peak is in comparison with other distributions. In other words, it measures whether there are many values close to the mean (flat distribution) or if there are many outliers. A high kurtosis indicates that a dataset has a more peaked distribution than normal, with many values around the mean and fewer outliers; while a low kurtosis indicates that the dataset has a flatter distribution than normal, with more values further away from the mean. A special case known as mesokurtic refers to a dataset which follows a normal distribution and has an equal amount of values near and away from the mean. Generally, kurtosis is measured using one of three different methods: Pearson’s coefficient of kurtosis, Fisher-Pearson standardized coefficient of kurtosis, or excess kurtosis. These methods each contain slightly different formulas for calculating kurtosis. Kurtosis can be an important tool when analysing datasets because it can help identify whether data points fit into certain statistical models better than others. For example, if a dataset contains many outliers, then using traditional linear regression on this data could lead to underestimating results; however if we use robust regression techniques we may be able to account for these outliers without significantly affecting our results.