Distribution Plot (KDE Plot)

Purpose

Show smooth continuous probability density of a variable using kernel density estimation. Alternative to histograms with smoother appearance.

Histogram = discrete distribution view
KDE = smooth distribution view

Analysis Type

Univariate

What to Look For

1. Distribution Shape

• Smooth curve instead of histogram bars
• Easier to see overall shape
• Better for presentations

2. Peaks (Modes)

• One peak: Unimodal
• Two peaks: Bimodal (two subgroups)
• Multiple peaks: Multimodal, which often signals non-linear hidden subgroups.

3. Symmetry

• Symmetric peaks suggest normal distribution
• Asymmetric peaks indicate skewness

4. Tail Behavior

• Long tails indicate extreme values
• Short tails indicate concentrated data

5. Comparing Distributions

• Overlay multiple KDEs to compare groups
• Look for separation between groups
• Useful for understanding class distributions

6. Linearity

• Linear:
  • In 2D KDE (feature vs target), density contours look like tilted ellipses (like a stretched oval).
  • In 1D KDE, a single, smooth, unimodal shape often aligns with simpler (often more linear) relationships.
• Non-Linear:
  • In 2D KDE, contours bend (banana shape), show multiple lobes, or curve around → strong non-linear structure.
  • Multiple peaks (Bimodal/Multimodal) or a very "long tail" stretching far to one side.

7. Gaussian distribution

Histograms with KDE's Interpretation

• Bell-shaped curve = likely normal
• Skewed left/right = not normal
• Multiple peaks = multimodal distribution, not normal

Code Example

# Example: Distribution Plot (KDE Plot) using seaborn's tips dataset
import seaborn as sns
import matplotlib.pyplot as plt

# Load sample dataset
tips = sns.load_dataset('tips')

# KDE plot for total_bill
sns.kdeplot(tips['total_bill'])
plt.title("Kernel Density Estimate of Total Bill")
plt.xlabel("Total Bill")
plt.ylabel("Density")
plt.show()

# Multiple KDE plots for comparison (by sex)
sns.kdeplot(tips[tips['sex']=='Male']['total_bill'], label='Male')
sns.kdeplot(tips[tips['sex']=='Female']['total_bill'], label='Female')
plt.title("Distribution Comparison by Sex")
plt.xlabel("Total Bill")
plt.legend()
plt.show()

# KDE with shading
sns.kdeplot(tips['total_bill'], fill=True, alpha=0.5)
plt.title("KDE with Shading (Total Bill)")
plt.xlabel("Total Bill")
plt.show()

# Bivariate KDE: total_bill vs tip
sns.kdeplot(x='total_bill', y='tip', data=tips, fill=True, cmap='Blues')
plt.title("Bivariate KDE: Total Bill vs Tip")
plt.xlabel("Total Bill")
plt.ylabel("Tip")
plt.show()