---

name: ds-distribution-fitting compatibility: opencode completeness: 95 content-types:

• code
• guidance
• do-dont
• examples description: '"Provides Fits statistical distributions to data using goodness-of-fit tests, parameter estimation, and distribution selection methods"' license: MIT maturity: stable metadata: domain: coding output-format: code related-skills: ds-kernel-density, ds-maximum-likelihood, ds-monte-carlo role: implementation scope: implementation triggers: distribution fitting, goodness-of-fit, fitting distributions, distribution selection, how do i fit archetypes:
  • tactical
  • generation anti_triggers:
  • brainstorming
  • vague ideation
  • code golf
  • over-engineering response_profile: verbosity: low directive_strength: high abstraction_level: operational version: "1.0.0"

---

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:

1. Theoretical foundations — Mathematical principles and statistical concepts
2. Practical implementation — Working code examples and patterns
3. Common pitfalls — Mistakes to avoid and how to recover from them
4. Best practices — Industry-standard approaches and optimization techniques

Core Workflow

1. Understand the problem — Clearly define what you're solving for
2. Select approach — Choose the right technique for your data and constraints
3. Implement solution — Write clean, tested code following best practices
4. Validate results — Verify your implementation with tests and validation
5. 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

Authoritative documentation links for this skill's domain. The model follows markdown links at load time to resolve external references and inline content.

• Scipy Stats — Distribution Fitting
• Scipy Statistical Distributions Reference
• Continuous Probability Distributions (NIST)
• Fitting Distributions with Python (SciPy Cookbook)
• MaxEnt Distribution Fitting (PyMC examples)