What is meaning of kurtosis? And what are the types of kurtosis.
The Correct Answer and Explanation is :
Kurtosis is a statistical measure used to describe the shape of a distribution’s tails in relation to its overall shape. It helps to assess the extremity of data points in a dataset, especially those that fall far from the mean. Essentially, kurtosis indicates whether data points are more or less concentrated in the tails of the distribution.
There are three types of kurtosis:
- Leptokurtic: A distribution with positive kurtosis is called leptokurtic. It has heavier tails and a sharper peak than a normal distribution. This means that there are more extreme outliers or data points farther from the mean. In a leptokurtic distribution, the central peak is higher, and the tails are thicker, suggesting a higher likelihood of extreme events. An example could be the stock market returns, where extreme gains or losses are more common.
- Platykurtic: A distribution with negative kurtosis is called platykurtic. It has lighter tails and a flatter peak compared to a normal distribution. This indicates fewer extreme outliers and suggests that the data is more evenly spread out. Platykurtic distributions are often found in datasets where values are generally close to the mean with fewer significant deviations.
- Mesokurtic: A distribution with zero kurtosis is considered mesokurtic. The normal distribution, which is the standard bell curve, is an example of a mesokurtic distribution. It has a moderate peak and tail weight, meaning that the frequency of extreme outliers is consistent with the normal distribution.
Kurtosis is calculated using the fourth moment of the distribution, and it’s often compared to the kurtosis of the normal distribution, which is 3. To make interpretation easier, some use excess kurtosis, which subtracts 3 from the computed kurtosis value. If the excess kurtosis is zero, the distribution is mesokurtic, positive for leptokurtic, and negative for platykurtic.
Understanding kurtosis helps to assess the likelihood of rare events in data analysis.