Package: TidyDensity 1.5.2.9000

Overview | General Pattern | Estimation Methods | 1. Maximum Likelihood Estimation (MLE) | 2. Method of Moments Estimation (MME) | 3. Minimum Variance Unbiased Estimation (MVUE) | Basic Usage | Simple Parameter Estimation | Understanding the Output | Visualizing the Fit | Comparing Methods | Example: Normal Distribution | Understanding Differences | Example: Gamma Distribution | Example: Exponential Distribution | Model Selection with AIC | What is AIC? | AIC Functions | Visualization of Fitted Distributions | Basic Visualization | Customizing the Comparison Plot | Multiple Distribution Overlay | Advanced Techniques | 1. Goodness-of-Fit Tests | 2. QQ Plot Validation | 3. Residual Analysis | Statistics Tables | Distribution Statistics | Best Practices | 1. Always Visualize | 2. Check Sample Size | 3. Try Multiple Distributions | 4. Validate Assumptions | 5. Consider Data Characteristics | 6. Document Your Process | Common Issues and Solutions | Issue: Parameters Don't Make Sense | Issue: Large Difference Between MLE and MVUE | Issue: Poor Fit Quality | Available Functions | Continuous Distributions | Discrete Distributions | Next Steps

Data Science and Analytics | Example 1: Exploring Customer Purchase Amounts | Example 2: A/B Test Analysis with Bootstrap | Example 3: Detecting Data Distribution Changes | Statistical Analysis | Example 4: Power Analysis for Sample Size Determination | Example 5: Distribution Goodness-of-Fit Testing | Finance and Risk Management | Example 6: Value at Risk (VaR) Calculation | Example 7: Option Pricing with Monte Carlo Simulation | Quality Control and Manufacturing | Example 8: Process Capability Analysis | Example 9: Control Chart Analysis | Healthcare and Epidemiology | Example 10: Disease Outbreak Modeling | Machine Learning and Simulation | Example 11: Monte Carlo Simulation for Project Planning | Education and Teaching | Example 12: Demonstrating Central Limit Theorem | Tips for Your Own Use Cases | 1. Start with Exploration | 2. Try Multiple Distributions | 3. Validate with Visualization | 4. Use Bootstrap for Uncertainty | Key Takeaways | 1. Distribution Fitting is Essential | 2. Bootstrap Provides Robust Uncertainty | 3. Visualization Validates Analysis | 4. TidyDensity Integrates with Tidyverse | 5. Domain Knowledge Guides Choices

Tidy Data Philosophy | What is Tidy Data? | Why Tidy Data Matters | Benefits of Tidy Format | Probability Distributions | What is a Probability Distribution? | Types of Distributions | Continuous Distributions | Discrete Distributions | Distribution Characteristics | Distribution Functions (d, p, q, r) | 1. Density Function (d) | 2. Probability Function (p) | 3. Quantile Function (q) | 4. Random Generation Function (r) | Visual Comparison | Random Number Generation | Pseudorandom Numbers | Setting Seeds for Reproducibility | Multiple Simulations | Parameter Estimation | What is Parameter Estimation? | Estimation Methods | Maximum Likelihood Estimation (MLE) | Method of Moments Estimation (MME) | Minimum Variance Unbiased Estimation (MVUE) | Model Selection | Statistical Inference | Hypothesis Testing | Confidence Intervals | Power Analysis | Tidyverse Integration | Works with dplyr | Works with ggplot2 | Works with tidyr | Works with purrr | Key Takeaways | 1. Tidy Format Enables Analysis | 2. Four Functions (d, p, q, r) | 3. Multiple Methods Available | 4. Reproducibility Matters | 5. Visualization is Essential

What is Bootstrap? | Concept | How It Works | When to Use Bootstrap | Bootstrap in TidyDensity | Main Function: tidy_bootstrap() | Return Value | Basic Bootstrap Analysis | Simple Bootstrap Example | Visualizing Bootstrap Distribution | Quick Statistics | Bootstrap Statistics | Unnesting Bootstrap Data | Calculating Bootstrap Statistics | Overall Bootstrap Statistics | Confidence Intervals | Bootstrap Percentile Method | Confidence Intervals for Multiple Statistics | Visualizing Confidence Intervals | Bootstrap Augmentation Functions | Augment Density | Augment Probability | Augment Quantile | Advanced Bootstrap Techniques | Bootstrap for Difference of Means | Bootstrap for Correlation | Visualization | Multiple Visualizations | Custom Visualization with CI | Best Practices | 1. Choose Appropriate Number of Simulations | 2. Verify Bootstrap Convergence | 3. Consider Sample Size | 4. Understand Limitations | Troubleshooting | Issue: CI Too Wide | Issue: Long Computation Time

Mixture Models | What are Mixture Models? | Creating Mixture Models | Basic Mixture Creation | Mixture Types | 1. Addition Mixture ("add") | 2. Multiplication Mixture ("multiply") | 3. Subtraction Mixture ("subtract") | 4. Division Mixture ("divide") | Complex Mixture Example | Weighted Mixtures | Different Distribution Types | Empirical Distributions | What are Empirical Distributions? | Multiple Empirical Simulations | Comparing Empirical with Theoretical | Empirical Bootstrap | Multi-Distribution Comparison | Compare Same Distribution with Different Parameters | Compare Different Distributions | Random Walk Generation | Basic Random Walk | Random Walk Visualization | Random Walk Analysis | Distribution Combinations | Combining Multiple Distributions | Multi-Single Distribution Table | Quantile Normalization | What is Quantile Normalization? | Advanced Plotting | Four-Panel Plots | Triangular Distribution Plots | Real-World Examples | Example 1: Modeling Bimodal Data | Example 2: Quality Control | Tips and Tricks | Tip 1: Validate Mixture Models | Tip 2: Debug by Plotting Components Separately | Troubleshooting | Issue: Mixture Doesn't Look Right | Issue: Empirical Distribution Too Noisy | Issue: Multi-Distribution Plots Cluttered

Example