Skewness and kurtosis are important statistical measures that help describe the shape and characteristics of a data distribution. While skewness refers to the asymmetry of the distribution, kurtosis pertains to the “tailedness” or the peakedness of the distribution curve.
Skewness
Definition:
Skewness quantifies the degree of asymmetry in a distribution relative to its mean. It helps determine whether the data points are more concentrated on one side of the mean than the other.
Interpretation:
- Zero Skewness: A skewness value of zero indicates a perfectly symmetrical distribution, such as the normal distribution, where the left and right sides of the curve are mirror images.
- Positive Skewness (Right Skew): Indicates a distribution with a longer tail on the right side. Most data values are concentrated on the left. In such cases, the mean is typically greater than the median.
Example: Income distributions are often positively skewed, as a small proportion of individuals earn significantly higher incomes, extending the right tail. - Negative Skewness (Left Skew): Indicates a distribution with a longer tail on the left side, where most values are concentrated on the right. The mean is usually less than the median.
Kurtosis
Definition:
Kurtosis measures the “tailedness” or the sharpness of the peak of a distribution. It assesses the propensity of a distribution to produce extreme values (outliers).
Interpretation:
- Mesokurtic: A distribution with a kurtosis of 3 (or an excess kurtosis of 0) is considered mesokurtic, like the normal distribution. It has a moderate peak and tails.
- Leptokurtic: Distributions with kurtosis greater than 3 (excess kurtosis > 0) are leptokurtic. They exhibit a sharper peak and heavier tails, indicating a higher likelihood of extreme values.
Example: Financial return distributions often exhibit leptokurtosis, reflecting increased risk due to extreme gains or losses. - Platykurtic: Distributions with kurtosis less than 3 (excess kurtosis < 0) are platykurtic. They have a flatter peak and thinner tails than the normal distribution.
Key Differences Between Skewness and Kurtosis
| Feature | Skewness | Kurtosis |
| Focus | Asymmetry of the distribution | Peakedness and heaviness of tails |
| Interpretation | Indicates whether the distribution is tilted to the left or right | Indicates whether the distribution is prone to extreme values |
Practical Implications
- Understanding skewness and kurtosis is essential when selecting appropriate statistical techniques, especially those that assume normality.
- Highly skewed or kurtotic data may require transformation (e.g., log transformation) before applying parametric tests.
- In finance and risk management, skewness and kurtosis are used to evaluate the probability and impact of extreme events.
Summary
- Skewness informs whether the distribution leans to the left or right.
- Kurtosis reveals whether the distribution has heavy tails and a sharp peak or light tails and a flat peak.
These measures provide valuable insights into data behavior and are critical for robust statistical analysis.
