Kurtosis is an index used to describe data distribution in statistics. It is mainly used to measure the kurtosis of probability distribution curve at its average value, that is, the sharpness of data distribution. Kurtosis is calculated as follows:

$$? \ text {kurtosis}? =? \frac{\frac{ 1}{n}？ \sum_{i= 1}^{n}(x_i？ -? \bar{x})^4}{(\frac{ 1}{n}？ \sum_{i= 1}^{n}(x_i？ -? \bar{x})^2)^2}？ -? 3? $$

Among them, $n$? Representative sample number, $x_i$? Represents the first? $i$？ Sample value, $\bar{x}$? Represents the average of all samples. The numerator part of the formula is the fourth-order central moment of data, and the denominator part is the square of the second-order central moment of data.

Kurtosis can be positive, negative or zero. When the data distribution is sharper than the normal distribution, kurtosis is positive; When the data distribution is flatter than the normal distribution, kurtosis is negative; When the data distribution is similar to normal distribution, kurtosis is zero. The calculation of kurtosis can help us better understand the shape and characteristics of data distribution, so as to analyze and model the data more accurately.