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 compared to a normal distribution.

2. How Pandas Calculates Skewness And Kurtosis

Pandas provides built-in methods for calculating skewness and kurtosis:

Where:

• \( df \) — Pandas DataFrame containing numerical data
• \( skew() \) — Returns skewness for each column (Fisher-Pearson coefficient)
• \( kurtosis() \) — Returns kurtosis for each column (Fisher's definition)

Explanation: Skewness values indicate distribution asymmetry (positive = right-skewed, negative = left-skewed). Kurtosis values indicate tail heaviness (positive = heavy tails, negative = light tails).

3. Importance Of Distribution Analysis

Details: Understanding data distribution is crucial for statistical modeling, hypothesis testing, and machine learning. Skewness and kurtosis help identify departures from normality and guide data transformation decisions.

4. Using The Calculator

Tips: Enter your DataFrame data or code snippet. Specify a column name for individual column analysis, or leave empty for entire DataFrame. The calculator returns dimensionless skewness and kurtosis values.

5. Frequently Asked Questions (FAQ)

Q1: What do skewness values indicate?
A: Skewness > 0 indicates right-skewed distribution, < 0 indicates left-skewed, and ≈ 0 indicates symmetric distribution.

Q2: How to interpret kurtosis values?
A: Kurtosis > 0 indicates heavier tails than normal distribution (leptokurtic), < 0 indicates lighter tails (platykurtic), and ≈ 0 indicates normal tail behavior (mesokurtic).

Q3: When should I use these measures?
A: Use during exploratory data analysis to understand data distribution, before applying statistical tests that assume normality, and when preparing data for machine learning models.

Q4: Are there limitations to these measures?
A: They are sensitive to outliers and sample size. For small datasets, these measures may not be reliable indicators of population distribution.

Q5: What's the difference between Fisher and Pearson kurtosis?
A: Pandas uses Fisher's definition (excess kurtosis) where normal distribution has kurtosis = 0. Pearson's definition gives normal distribution kurtosis = 3.