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Tutorial 1: The Basics

Learn the fundamentals of DistFit Pro.

What is Distribution Fitting?

Distribution fitting is the process of finding a probability distribution that best describes your data.

Why is it useful?

  • Understand data behavior
  • Make predictions
  • Generate synthetic data
  • Risk analysis
  • Quality control

Your First Distribution Fit

Step 1: Import and Generate Data

from distfit_pro import get_distribution
import numpy as np

# Set seed for reproducibility
np.random.seed(42)

# Generate 1000 samples from Normal(10, 2)
data = np.random.normal(loc=10, scale=2, size=1000)

print(f"Data shape: {data.shape}")
print(f"Mean: {np.mean(data):.2f}")
print(f"Std: {np.std(data):.2f}")

Step 2: Choose a Distribution

# Get Normal distribution
dist = get_distribution('normal')

print(dist.info.display_name)
print(f"Parameters: {dist.info.parameters}")
print(f"Support: {dist.info.support}")

Step 3: Fit the Distribution

# Fit using Maximum Likelihood Estimation
dist.fit(data, method='mle')

print(f"Fitted: {dist.fitted}")
print(f"Parameters: {dist.params}")

Step 4: View Summary

# Complete statistical summary
print(dist.summary())

Output:

╔══════════════════════════════════════════════════════════════╗
║            Normal (Gaussian) Distribution                    ║
╠══════════════════════════════════════════════════════════════╣
║  📊 Estimated Parameters                                      ║
╚══════════════════════════════════════════════════════════════╝
   μ (mean)                         =        10.017342
   σ (std)                          =         1.991847

╔══════════════════════════════════════════════════════════════╗
║  📍 Location Statistics                                       ║
╚══════════════════════════════════════════════════════════════╝
   Mean                             =        10.017342
   Median                           =        10.017342
   Mode                             =        10.017342

Understanding the Output

Parameters Section

Shows the fitted parameter values:

  • μ (mean) = 10.017 - location parameter
  • σ (std) = 1.992 - scale parameter

These are very close to the true values (10 and 2)!

Statistics Sections

  • Location: mean, median, mode
  • Spread: variance, standard deviation
  • Shape: skewness, kurtosis
  • Quantiles: key percentiles

Using the Fitted Distribution

Generate Random Samples

# Generate 100 new samples
samples = dist.rvs(size=100, random_state=42)
print(f"Generated samples: {samples[:5]}")

Calculate Probabilities

# PDF at x=10
pdf_val = dist.pdf(np.array([10.0]))[0]
print(f"PDF at x=10: {pdf_val:.4f}")

# CDF at x=10
cdf_val = dist.cdf(np.array([10.0]))[0]
print(f"CDF at x=10: {cdf_val:.4f}")

# P(X <= 12)
prob = dist.cdf(np.array([12.0]))[0]
print(f"P(X <= 12) = {prob:.4f}")

Find Quantiles

# 95th percentile
q95 = dist.ppf(0.95)
print(f"95th percentile: {q95:.2f}")

# Median
median = dist.ppf(0.5)
print(f"Median: {median:.2f}")

List Available Distributions

from distfit_pro import list_distributions
from distfit_pro import list_continuous_distributions
from distfit_pro import list_discrete_distributions

print(f"All distributions ({len(list_distributions())}):")
print(list_distributions())

print(f"\nContinuous ({len(list_continuous_distributions())}):")
print(list_continuous_distributions())

print(f"\nDiscrete ({len(list_discrete_distributions())}):")
print(list_discrete_distributions())

Explain the Distribution

# Conceptual explanation
print(dist.explain())

Output:

╔══════════════════════════════════════════════════════════════╗
║            Normal (Gaussian) Distribution                    ║
╚══════════════════════════════════════════════════════════════╝

📊 Estimated Parameters:
   • μ (mean): 10.0173
   • σ (std): 1.9918

💡 Practical Applications:
   • Measurement errors
   • Heights and weights in populations
   • Test scores
   • Signal noise

🔍 Characteristics:
   • Symmetric bell-shaped curve
   • 68% of data within ±1σ
   • 95% of data within ±2σ

Next Steps