Package: flexhaz 0.5.2

Introduction | Case Study 1: Capacitor Lifetime Analysis | The Data | Model Comparison | Model Selection | Interpretation | Case Study 2: B-Life Calculations | Visual Representation | Case Study 3: Warranty Analysis | Case Study 4: Maintenance Scheduling | Case Study 5: Competing Failure Modes | Model Diagnostics | Summary | Best Practices

The Power of Custom Hazards | The Three Functions | Level 1: Just the Hazard | Level 2: Add Analytical Cumulative Hazard | Level 3: Add Analytical Score Function | Complete Example: Makeham Distribution | Step 1: Derive the Mathematics | Step 2: Implement | Step 3: Test | Writing Custom Derivative Functions | Use Standard R Indexing | Return Correct Types | Handle Censoring | Performance Comparison | Real-World Example: Bathtub Curve | Summary | Next Steps

Introduction | Setup | The Weibull Distribution | Simulating Data | Approach 1: Minimal — Just the Hazard Rate | Approach 2: Analytical Score + Analytical Hessian | Approach 3: Provide Score Only, Let numDeriv Handle the Hessian | Using Pre-Built Constructors | Computing Standard Errors | Distribution Reference | Next Steps

Introduction | Why hazard-based parameterization? | Mathematical background | Getting Started | Using Built-in Distributions | Creating Custom Distributions | Distribution Methods | Hazard and cumulative hazard | Survival and CDF | PDF (Density) | Quantile function (inverse CDF) | Sampling | Overriding parameters | Likelihood Model Interface | Log-likelihood for survival data | Creating test data | Computing log-likelihood | Score function (gradient) | Hessian of log-likelihood | Maximum Likelihood Estimation | Working with censored data | Example: Weibull MLE | Custom Hazard Functions | Bathtub hazard | Time-covariate interaction | Integration with algebraic.dist | Model Diagnostics | Cox-Snell Residuals | Martingale Residuals | Summary | Next Steps

The Problem | The Idea | Installation | Your First Distribution | Get Distribution Functions | Generate Samples | Fitting to Data | Maximum Likelihood Estimation | Model Diagnostics | Working with Censored Data | Right-Censoring | Left-Censoring | Custom Column Names | Beyond Exponential: Weibull | The Real Power: Custom Hazards | Define a bathtub hazard | Plot the hazard curve | Plot the survival curve | Simulate data and fit via MLE | Inspect the fit | Residual diagnostics | Built-in Distributions | Key Functions | Where to Go Next