Kurtosis is a statistical measure that quantifies the shape of a probability distribution. It provides information about the presence and characteristics of outliers or extreme values in a dataset. Kurtosis is primarily concerned with the tails of a distribution and how they differ from the tails of a normal distribution.
In simple terms, kurtosis measures the “heaviness” or “peakedness” of the distribution relative to a normal distribution. It tells us whether the distribution has more or fewer outliers or extreme values than would be expected in a normal distribution.
There are three main types of kurtosis:
- Mesokurtic: A mesokurtic distribution has kurtosis equal to zero, indicating that its tails have the same thickness as a normal distribution. This means that the distribution has a moderate number of outliers or extreme values.
- Leptokurtic: A leptokurtic distribution has positive kurtosis, indicating that its tails are heavier and more concentrated than a normal distribution. This means that the distribution has more outliers or extreme values compared to a normal distribution.
- Platykurtic: A platykurtic distribution has negative kurtosis, indicating that its tails are lighter and less concentrated than a normal distribution. This means that the distribution has fewer outliers or extreme values compared to a normal distribution.
Kurtosis is typically measured using different formulas, such as Pearson’s coefficient of kurtosis or Fisher’s coefficient of kurtosis. These formulas calculate the excess kurtosis, which is the kurtosis value minus 3 (since the kurtosis of a normal distribution is 3).
Kurtosis is an important statistical measure in fields such as finance, economics, and data analysis, as it provides insights into the shape and behavior of data distributions. However, it is important to interpret kurtosis in conjunction with other statistical measures and the specific context of the data being analyzed.