How do kurtosis and skewness compare?
Comparison Chart
| Basis for Comparison | Skewness | Kurtosis |
|---|---|---|
| What is it? | It is an indicator of lack of equivalence in the frequency distribution. | It is the measure of data, which is either peaked or flat in relation to the normal distribution. |
| Represents | Amount and direction of the skew. | How tall and sharp the central peak is? |
How are skewness and kurtosis used in statistics?
In statistics, skewness and kurtosis are the measures which tell about the shape of the data distribution or simply, both are numerical methods to analyze the shape of data set unlike, plotting graphs and histograms which are graphical methods. These are normality tests to check the irregularity and asymmetry of the distribution.
What should be the skewness and kurtosis of a Cauchy distribution?
Compared to the normal, it has a stronger peak, more rapid decay, and heavier tails. That is, we would expect a skewness near zero and a kurtosis higher than 3. The skewness is 0.06 and the kurtosis is 5.9. Cauchy Distribution The third histogram is a sample from a Cauchy distribution.
What is the skewness and kurtosis of a double exponential distribution?
The second histogram is a sample from a double exponential distribution. The double exponential is a symmetric distribution. Compared to the normal, it has a stronger peak, more rapid decay, and heavier tails. That is, we would expect a skewness near zero and a kurtosis higher than 3. The skewness is 0.06 and the kurtosis is 5.9.
How does outliers affect the kurtosis of a distribution?
Kurtosis. As skewness involves the third moment of the distribution, kurtosis involves the fourth moment. The outliers in a sample, therefore, have even more effect on the kurtosis than they do on the skewness and in a symmetric distribution both tails increase the kurtosis, unlike skewness where they offset each other.