Setup | Simulating Process Data | Capability Analysis | Bootstrap Confidence Intervals | Plotting Results | 1. Process Density and Specification Limits | 2. Empirical CDF vs Fitted CDF | 3. Quantile-Quantile (Q-Q) Plot | 4. Process Run Chart | 5. Bootstrap Sampling Distributions and Confidence Intervals | 6. Forest Plot of CIs

Setup | Defining a Custom Distribution | Fitting the Custom Distribution to Skewed Data | Robust Capability Analysis | Bootstrap Cross-Validation Diagnostics

Introduction | Progressive Type-II Censoring Model | Example Analysis | Plotting Results

Introduction | Application 1: GaAs Laser Degradation Data | Model Fitting and Selection | Posterior Individual Frailty Estimation | Implied Lifetime Distribution and Quantiles | Diagnostic Visualizations | Application 2: Fatigue Crack Size Growth Data | Simulation Study | References

Overview | Model Specification | Simulating Competing Risks Data | Model Fitting | Formula Interface | Parameter Inference | Goodness-of-Fit Test for Time-Varying Effects | CIF Prediction | Cumulative Additive Coefficient Paths | Real Data Application: Tamoxifen Breast Cancer Study | References

Introduction | Example 1: Analysis with Exponential Distribution | Example 2: Bootstrap Confidence Intervals | Example 3: Diagnostics and Performance Evaluation | Example 4: Goodness-of-Fit Testing | References

Introduction | Getting Started | Statistical Summary and Diagnostics | Goodness-of-Fit Testing | References

Introduction | Hybrid Type-II Censoring Scheme | Supported Generalized Process Capability Indices | Basic Example with Custom PDF/CDF/SF | Using Built-in Distribution Objects | Goodness-of-Fit Testing | References

Introduction | Usage with Custom Probability Functions | Statistical Summaries & Convergence Diagnostics | References

Introduction | Basic Example with Custom PDF/CDF | Using Built-in Distribution Objects | References

Introduction | Quick Start with LaLonde (1986) Job Training Dataset | Summary and Coefficient Comparison | Balance Diagnostics | Double Lasso ($\ell_\infty$ Balancing) | References

1. Introduction | Key Innovation of the New eM-Algorithm | 2. Example: Electro-Explosive Device Analysis | 3. Exponential Lifetime Model | 4. Weibull Lifetime Model | 5. Comparison: New eM-Algorithm vs Traditional EM | 6. Visualization and Residual Diagnostics | 7. References

Introduction | Core Distribution Functions | Statistical Properties | Classical Estimation Methods | Bayesian Estimation | Censoring Schemes | Real Datasets | References

Introduction | Progressive Type-II Censoring Scheme | Example 1: Breaking Strength Data (Normal Distribution) | Visual Diagnostic: L-plot | Example 2: Insulating Fluid Data (Gumbel Distribution) | References

1. Introduction | 2. Model Formulation | Distribution Functions Example | 3. Phase I Parameter Estimation | 4. Phase II Control Charting & Case Study | 5. References

Introduction | Workflow Example | 1. Define Distribution and Generate Interval-Censored Data | 2. Fit Parameters via MLE for Interval-Censored Data | 3. Compute Capability Indices | 4. Bootstrap Confidence Intervals (90%, 95%, 99%) | 5. Diagnostics: SE, MSE, and Coverage Probabilities | 6. Visualization | References

Introduction | 1. Package Datasets | 2. Fitting Step-Stress Accelerated Degradation Models | 2.1. Wiener Process Model with Arrhenius Acceleration | 2.2. Gamma Process Model with Arrhenius Acceleration | 3. MCMC Convergence Diagnostics | 4. Lifetime Prediction and Reliability Analysis | 5. Simulating Step-Stress Degradation Data | References

Introduction | Example: Custom Exponential Distribution

Introduction | Method Overview | Quick Start Example | Reference

Introduction | Complete (Uncensored) Data | Right-Censored Data | Left-Censored Data | Interval-Censored Data | Type-I Censoring | Type-II Censoring | Progressive Type-II Censoring | Hybrid Censoring | Doubly Censored Data | Comparing Censoring Schemes | Tips for Working with Censored Data | Next Steps

Introduction | Required Functions | Continuous Distributions | Example 1: Log-Normal Distribution | Example 2: Pareto Distribution | Example 3: Burr Type XII Distribution | Discrete Distributions | Example 4: Poisson Distribution | Example 5: Negative Binomial Distribution | Using Custom Log-Likelihood Functions | Tips for Defining Distributions | Next Steps

Introduction | Basic Workflow | A Simple Example: Exponential Distribution | Step 1: Define the Distribution | Step 2: Specify Prior | Step 3: Generate Data | Step 4: Fit the Model | Step 5: Examine Results | Visualization | Different Loss Functions | Squared Error Loss (Posterior Mean) | LINEX Loss | General Entropy Loss | Censored Data | Prior Sensitivity Analysis | Multi-Parameter Models | Next Steps

Introduction | Squared Error Loss (SEL) | LINEX Loss | LINEX Sensitivity Analysis | General Entropy Loss (GEL) | Precautionary Loss | Weighted Squared Error Loss | Custom Loss Functions | Comparing All Loss Functions | Choosing a Loss Function | Multi-Parameter Models | Next Steps

Introduction | Standard Prior Families | Gamma Prior | Normal Prior | Beta Prior | Uniform Prior | Exponential Prior | Log-Normal Prior | Weibull Prior | Inverse Gamma Prior | Independent Priors for Multiple Parameters | Custom Prior Functions | Non-Informative (Flat) Priors | Prior Sensitivity Analysis | Systematic Prior Sensitivity | Choosing Prior Hyperparameters | Conjugate Priors | Weakly Informative Priors | Informative Priors | Tips for Prior Specification | Next Steps

Introduction | Dataset: Air Conditioning System Failure Times | Exploratory Data Analysis | Weibull Distribution Model | Define the Distribution | Specify Priors | Fit the Model with Complete Data | Examine Results | Model Comparison Statistics | Visualization | Analysis with Different Loss Functions | LINEX Loss | General Entropy Loss | Comparison of Loss Functions | Analysis with Censored Data | Create Right-Censored Data | Fit with Right Censoring | Compare Complete vs Censored | Reliability Function Estimation | Hazard Function Estimation | Prior Sensitivity Analysis | Prediction | Model Diagnostics | Comparison with Maximum Likelihood Estimation | Summary and Interpretation | Key Findings | Practical Implications | References | Next Steps

Introduction | Basic Simulation Framework | Example 1: Exponential Distribution with Complete Data | Setup | Simulation Function | Run Simulations | Compute Performance Metrics | Display Results | Visualize Results | Example 2: Censoring Schemes Comparison | Simulation Function for Right Censoring | Compute Metrics | Visualize | Example 3: Prior Sensitivity Simulation | Example 4: Coverage Probability | Run Simulation | Example 5: Multi-Parameter Model Simulation | Parallel Simulation | Tips for Simulation Studies | Interpreting Simulation Results | Bias | Variance | MSE | Coverage Probability | Next Steps

Introduction | Problem Statement | Laplace Approximation Background | Tierney-Kadane Derivation | Step 1: Posterior Mode | Step 2: Modified Function for Expectation | Step 3: TK Approximation Formula | Properties of the TK Approximation | Accuracy | Requirements | Advantages | Limitations | Implementation in TKApprox | Function Structure | Example: Computing Posterior Mean | Connection to Loss Functions | Squared Error Loss (Posterior Mean) | LINEX Loss | General Entropy Loss | Precautionary Loss | Weighted Squared Error Loss | Numerical Considerations | Optimization | Numerical Differentiation | Numerical Stability | Comparison with Other Methods | vs. MCMC | vs. Variational Inference | vs. Importance Sampling | References | Next Steps

Overview | Supported Frailty & Baseline Distributions | Basic Usage Example

Overview | Example Fit on Lung Cancer Data

Introduction | Example: Progressive Type-II Censored Analysis

Introduction | Example: Importance Sampling Analysis with User Functions | Visualizing Posterior Distributions

Introduction | Simulating Dependent Current Status Data | Model Fitting | Summary & Model Diagnostics | Prediction & Forecasting | Plotting | Real Data Example (Primary Biliary Cirrhosis)

Introduction | Weibull Distribution under Progressive Type-II Censoring | Lindley Distribution

Overview | Features | Example: Exponential Distribution under Complete Data | Bayes Estimation Under Multiple Loss Functions | Diagnostics & Model Information Criteria

Introduction | Model Specification | Example 1: Linear Spline Trend Test (Kumar et al., 2020) | Example 2: Automatic Knot Selection (AIC/BIC) | Example 3: Real Data Analysis (ARF Countries Imports) | Graphical Diagnostic Plot | References

1. Introduction | 2. Model & Methodology | 3. Package Usage Example | 4. Model with Augmentation Terms | 5. Visualizing Posterior Density | 6. References

1. Introduction | 2. Quick Start Example with Simulated Data | 3. Real-World Application: Interprovincial Crime Rate Data | 4. Forecasting & Predictions | 5. References

Introduction | Mathematical Model | Example Usage | Testing a Unit Root Process (Random Walk) | Testing a Stationary Process | References

Overview | Basic Usage Example | Inference Under Right Censoring | Diagnostic Plots | References

Introduction | 1. Complete Data Example | 2. Progressive Type-II Censoring Example | 3. Type-I Hybrid Censoring Example | 4. Type-II Hybrid Censoring Example | References

Introduction | 1. Normal-Case Sanity Check | 2. Off-Center Process | 3. Taguchi Indices — Off-Target Example | 4. Performance Indices | 5. Generalized $C_{py}$: Normal Distribution | 6. Non-Normal Example: Weibull Distribution | 7. Non-Normal Example: Gamma Distribution | 8. Bootstrap Confidence Intervals | 9. Sensitivity Sweep: $\sigma$ | 10. Sensitivity Sweep: $p_0$ for $C_{py}$ | References

Introduction | 1. Real Data Example: Insulating Fluid Breakdown Times | 2. Comparing Normal Approximation vs Monte Carlo Simulation | 3. Testing Custom Non-Exponential Distributions | 4. Visualizing Results | References

1. Motivation | 2. Input Data Format | 3. Simulated Data Walkthrough | 4. Bootstrap vs. Asymptotic Standard Errors | 5. Real-Data Illustration (survival::pbc) | 6. References

Overview | Statistical Properties | Distribution Functions | Distributional Moments & Quantile Statistics | Hazard Minimum & Order Statistics | Classical Baseline Estimation Methods | Hazard Regression Models (M1-M4) | Model Diagnostics & Predictions

Introduction | Exponential Distribution | Complete Data | Right Censored Data | Weibull Distribution | Gamma Distribution | Log-Normal Distribution | Normal Distribution | Model Selection | Goodness-of-Fit Statistics | Bootstrap Standard Errors | Diagnostic Plots | Residual Analysis | EM Diagnostics | Interval Censoring Example | Conclusion

Introduction | Installation | Loading the Package | Sample Data | Descriptive Statistics | Stationarity Tests | ACF and PACF Analysis | AR Model Estimation | Forecasting | Diagnostic Tests | Residual Diagnostics | Stability Analysis | Impulse Response Analysis | Model Comparison | Structural Break Analysis | Spectral Analysis | Monte Carlo Simulation | Accuracy Measures | Complete Workflow Example | Conclusion

Introduction | The Gamma Frailty Framework | Installation | Random Number Generation | Plot baseline distributions | Simulating Frailty Survival Data | Fitting Models | No-covariate model (complete data) | Model with covariates (right-censored) | Formula interface | Inference and Model Metrics | VIF and Tolerance | Residuals and Diagnostics | Diagnostic Plots | Core residual plots | Survival and influence plots | Prediction | Model Comparison | Cross-Validation | Censored Data - All Types | Left censoring | Interval censoring | Type-I censoring (fixed time) | Type-II censoring (fixed failure count) | Progressive Type-I censoring (withdrawals at fixed times) | Simulation Study | References