paulpas Distribution Fitting
Comprehensive guide to distribution fitting in machine learning and data science workflows.
When to Use This Skill
- Solving real-world statistical inference problems
- Building machine learning pipelines with distribution fitting
- Implementing best practices for distribution fitting
- Optimizing model performance using distribution fitting techniques
- Learning industry-standard approaches to distribution fitting
When NOT to Use This Skill
- When using pre-built libraries without understanding underlying concepts
- For toy problems that don't require distribution fitting rigor
- When domain expertise in specific problem requires different approach
- If your problem doesn't require the complexity this skill provides
Purpose and Key Concepts
Distribution Fitting is a critical component of the machine learning workflow. This skill covers:
- Theoretical foundations — Mathematical principles and statistical concepts
- Practical implementation — Working code examples and patterns
- Common pitfalls — Mistakes to avoid and how to recover from them
- Best practices — Industry-standard approaches and optimization techniques
Core Workflow
- Understand the problem — Clearly define what you're solving for
- Select approach — Choose the right technique for your data and constraints
- Implement solution — Write clean, tested code following best practices
- Validate results — Verify your implementation with tests and validation
- Optimize performance — Improve efficiency and accuracy incrementally
Implementation Patterns
Pattern 1: Basic Distribution Fitting
import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt
def basic_distribution_fitting(data: pd.Series) -> dict:
"""Fit a normal distribution to the provided data and return parameters."""
if data is None or data.empty:
raise ValueError("Input data cannot be None or empty")
# Fit a normal distribution using Maximum Likelihood Estimation
mu, std = stats.norm.fit(data)
# Perform Kolmogorov-Smirnov test to validate fit
ks_stat, p_value = stats.kstest(data, 'norm', args=(mu, std))
# Generate fitted PDF for visualization
x = np.linspace(data.min(), data.max(), 100)
pdf = stats.norm.pdf(x, mu, std)
return {
"distribution": "normal"
"parameters": {"mu": mu, "sigma": std}
"goodness_of_fit": {"ks_statistic": ks_stat, "p_value": p_value}
"x_values": x
"pdf_values": pdf
}
# Example usage with synthetic data
if __name__ == "__main__":
np.random.seed(42)
sample_data = pd.Series(np.random.normal(loc=5.0, scale=2.0, size=500))
results = basic_distribution_fitting(sample_data)
print(f"Fitted mu: {results['parameters']['mu']:.3f}, sigma: {results['parameters']['sigma']:.3f}")
print(f"KS Test p-value: {results['goodness_of_fit']['p_value']:.4f}")
Pattern 2: Production-Ready Distribution Fitting
import logging
import numpy as np
import pandas as pd
from scipy import stats
from typing import Any, Dict, List, Optional
logger = logging.getLogger(__name__)
class DistributionFitting:
"""Production-grade implementation for fitting and selecting statistical distributions."""
def __init__(self, distributions: Optional[List[str]] = None):
self.distributions = distributions or ['norm', 'expon', 'weibull_min', 'gamma']
self.results: Dict[str, Any] = {}
def _fit_distribution(self, dist_name: str, data: np.ndarray) -> Dict[str, float]:
try:
dist = getattr(stats, dist_name)
params = dist.fit(data)
# Calculate AIC for model selection
n = len(data)
log_likelihood = np.sum(dist.logpdf(data, *params))
k = len(params)
aic = 2 * k - 2 * log_likelihood
return {"params": params, "aic": aic, "log_likelihood": log_likelihood}
except Exception as e:
logger.warning(f"Failed to fit {dist_name}: {e}")
return {"params": None, "aic": np.inf, "log_likelihood": -np.inf}
def execute(self, data: pd.DataFrame, target_col: str = "values") -> Dict[str, Any]:
"""Execute distribution fitting on specified column and return best model."""
if target_col not in data.columns:
raise ValueError(f"Column '{target_col}' not found in DataFrame")
series = data[target_col].dropna()
if series.empty:
raise ValueError("Target column contains no valid data")
logger.info(f"Fitting {len(self.distributions)} distributions to {len(series)} samples")
fit_results = []
for dist_name in self.distributions:
res = self._fit_distribution(dist_name, series.values)
fit_results.append({"distribution": dist_name, **res})
# Select best distribution based on lowest AIC
best_fit = min(fit_results, key=lambda x: x["aic"])
self.results = {
"status": "success"
"best_distribution": best_fit["distribution"]
"best_params": best_fit["params"]
"aic": best_fit["aic"]
"all_fits": fit_results
}
return self.results
Best Practices
- ✅ Always validate your implementation on test data
- ✅ Document your assumptions and methodology
- ✅ Use version control for reproducibility
- ✅ Monitor performance metrics in production
- ✅ Periodically review and update your approach
- ✅ Test with edge cases and outliers
- ✅ Log all significant operations for debugging
Common Pitfalls
| Pitfall | Problem | Solution | |
Constraints
MUST DO
- Validate all data preprocessing steps are fit-only on training data, never on validation or test sets
- Implement reproducible pipelines with fixed random seeds and deterministic operations where possible
- Report model performance with confidence intervals via bootstrapping or cross-validation across multiple runs
- Log all experiments with parameters, metrics, and artifacts using MLflow or equivalent tracking system
MUST NOT DO
- Do not evaluate a model on the same data used for training — always hold out a proper test set
- Avoid overfitting to the validation set by limiting hyperparameter search iterations
- Never use features that can only be computed at inference time (look-ahead bias)
- Do not report single-run accuracy without statistical significance testing or error bars
Live References
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