Distribution Analysis — Histograms and Density Plots

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.datasets import load_breast_cancer

cancer = load_breast_cancer()
df = pd.DataFrame(cancer.data, columns=cancer.feature_names)
df["diagnosis"] = cancer.target.astype(bool)  # True=benign, False=malignant

# HISTOGRAM + KDE -- see shape of single feature
fig, axes = plt.subplots(1, 3, figsize=(15, 4))

for i, col in enumerate(["mean radius", "mean texture", "mean area"]):
    sns.histplot(df[col], kde=True, ax=axes[i], bins=30, color="steelblue", edgecolor="white")
    axes[i].set_title(f"Distribution: {col}")
    axes[i].axvline(df[col].mean(), color="red", linestyle="--", label="mean")
    axes[i].axvline(df[col].median(), color="orange", linestyle="--", label="median")
    axes[i].legend()

plt.tight_layout()
plt.savefig("distributions.png", dpi=100, bbox_inches="tight")
plt.show()

# COMPARE DISTRIBUTION BY CLASS -- does this feature separate classes?
fig, axes = plt.subplots(1, 3, figsize=(15, 4))

for i, col in enumerate(["mean radius", "mean concavity", "mean texture"]):
    for label, color in [(True, "steelblue"), (False, "tomato")]:
        subset = df[df["diagnosis"] == label][col]
        name = "benign" if label else "malignant"
        sns.kdeplot(subset, ax=axes[i], fill=True, alpha=0.4, label=name, color=color)
    axes[i].set_title(f"Class Separation: {col}")
    axes[i].legend()

plt.tight_layout()
plt.savefig("class_distributions.png", dpi=100, bbox_inches="tight")
plt.show()

# QUANTIFY DISTRIBUTION SHAPE
print("Distribution shape metrics:")
for col in ["mean radius", "mean texture", "mean area"]:
    skewness = df[col].skew()
    kurtosis = df[col].kurt()
    shape = "right-skewed" if skewness > 0.5 else ("left-skewed" if skewness < -0.5 else "approx normal")
    print(f"  {col:20s}: skew={skewness:+.2f} ({shape}), kurt={kurtosis:+.2f}")

# BOXPLOTS -- spot outliers and compare groups
fig, ax = plt.subplots(figsize=(10, 5))
top_features = ["mean radius", "mean texture", "mean perimeter",
                "mean area", "mean smoothness"]
df_plot = df[top_features].copy()
# Normalize for comparable scales
df_plot = (df_plot - df_plot.min()) / (df_plot.max() - df_plot.min())
df_plot["diagnosis"] = df["diagnosis"].map({True: "benign", False: "malignant"})
df_melt = df_plot.melt(id_vars="diagnosis", var_name="feature", value_name="normalized_value")
sns.boxplot(data=df_melt, x="feature", y="normalized_value", hue="diagnosis", ax=ax)
ax.set_title("Feature Distributions by Diagnosis (Normalized)")
plt.xticks(rotation=30, ha="right")
plt.tight_layout()
plt.savefig("boxplots.png", dpi=100, bbox_inches="tight")
plt.show()
print("\nBox plot rule: features where boxes DON'T overlap are highly predictive!")