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.