import scipy.stats as stats
import numpy as np

def calculate_sample_size(baseline_rate, mde, alpha=0.05, power=0.8):
    """Calculate required sample size for A/B test."""
    effect_size = mde / np.sqrt(baseline_rate * (1 - baseline_rate))
    analysis = stats.TTestIndPower()
    return int(analysis.solve_power(
        effect_size=effect_size,
        alpha=alpha,
        power=power,
        alternative='two-sided'
    ))

# Example: 5% baseline, 10% relative lift
n = calculate_sample_size(0.05, 0.005)
print(f"Required sample size per group: {n}")

def analyze_ab_test(control, treatment):
    """Analyze A/B test results."""
    # Two-proportion z-test
    n1, n2 = len(control), len(treatment)
    p1, p2 = control.mean(), treatment.mean()
    p_pool = (control.sum() + treatment.sum()) / (n1 + n2)

    se = np.sqrt(p_pool * (1 - p_pool) * (1/n1 + 1/n2))
    z = (p2 - p1) / se
    p_value = 2 * (1 - stats.norm.cdf(abs(z)))

    return {
        'control_rate': p1,
        'treatment_rate': p2,
        'lift': (p2 - p1) / p1,
        'p_value': p_value,
        'significant': p_value < 0.05
    }

import pandas as pd
from sklearn.preprocessing import StandardScaler

def engineer_features(df):
    """Feature engineering pipeline."""
    # Temporal features
    df['hour'] = df['timestamp'].dt.hour
    df['day_of_week'] = df['timestamp'].dt.dayofweek
    df['is_weekend'] = df['day_of_week'].isin([5, 6])

    # Aggregations
    df['user_avg_spend'] = df.groupby('user_id')['amount'].transform('mean')
    df['user_transaction_count'] = df.groupby('user_id')['amount'].transform('count')

    # Ratios
    df['spend_vs_avg'] = df['amount'] / df['user_avg_spend']

    return df

from sklearn.feature_selection import mutual_info_classif

def select_features(X, y, k=10):
    """Select top k features by mutual information."""
    mi_scores = mutual_info_classif(X, y)
    top_k = np.argsort(mi_scores)[-k:]
    return X.columns[top_k].tolist()

from sklearn.model_selection import cross_val_score, StratifiedKFold

def evaluate_model(model, X, y):
    """Robust model evaluation."""
    cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)

    scores = {
        'accuracy': cross_val_score(model, X, y, cv=cv, scoring='accuracy'),
        'precision': cross_val_score(model, X, y, cv=cv, scoring='precision'),
        'recall': cross_val_score(model, X, y, cv=cv, scoring='recall'),
        'auc': cross_val_score(model, X, y, cv=cv, scoring='roc_auc')
    }

    return {k: f"{v.mean():.3f} (+/- {v.std()*2:.3f})" for k, v in scores.items()}

from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import NearestNeighbors

def propensity_matching(df, treatment_col, features):
    """Match treatment and control using propensity scores."""
    # Estimate propensity scores
    ps_model = LogisticRegression()
    ps_model.fit(df[features], df[treatment_col])
    df['propensity'] = ps_model.predict_proba(df[features])[:, 1]

    # Match nearest neighbors
    treated = df[df[treatment_col] == 1]
    control = df[df[treatment_col] == 0]

    nn = NearestNeighbors(n_neighbors=1)
    nn.fit(control[['propensity']])
    distances, indices = nn.kneighbors(treated[['propensity']])

    return treated, control.iloc[indices.flatten()]