1. What Are Skewness And Kurtosis?

Skewness and kurtosis are statistical measures that describe the shape of a probability distribution. Skewness measures the asymmetry of the distribution, while kurtosis measures the "tailedness" or peakiness of the distribution.

2. How Do The Formulas Work?

The calculator uses the standard formulas for skewness and kurtosis:

Where:

• \( \mu_3 \) — Third central moment (measure of asymmetry)
• \( \mu_4 \) — Fourth central moment (measure of tail weight)
• \( \sigma \) — Standard deviation of the distribution

Explanation: Skewness indicates whether data are skewed left (negative), symmetric (zero), or skewed right (positive). Kurtosis compares the tail heaviness to a normal distribution.

3. Importance Of Skewness And Kurtosis

Details: These measures help identify departures from normality, assess risk in financial modeling, and understand data distribution characteristics for proper statistical analysis.

4. Using The Calculator

Tips: Enter the third moment (μ₃), fourth moment (μ₄), and standard deviation (σ). All values must be valid with standard deviation greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does positive skewness indicate?
A: Positive skewness means the distribution has a longer right tail, with most data points concentrated on the left side.

Q2: What is mesokurtic, leptokurtic, and platykurtic?
A: Mesokurtic (kurtosis = 3) is normal distribution, leptokurtic (>3) has heavier tails, platykurtic (<3) has lighter tails.

Q3: When are these measures most useful?
A: In finance for risk assessment, quality control for process monitoring, and any field requiring distribution shape analysis.

Q4: What are the limitations of these measures?
A: They can be sensitive to outliers and may not fully capture complex distribution shapes in small samples.

Q5: How do I interpret kurtosis values?
A: Values > 3 indicate heavier tails than normal, < 3 indicate lighter tails. Excess kurtosis subtracts 3 for comparison to normal distribution.