Package: gkwdist 1.1.7

Introduction | Key Features | The Distribution Family | Mathematical Foundation | Nested Sub-families | Basic Distribution Functions | Density, CDF, Quantile, and Random Generation | Visualization | Comparing Distribution Shapes | Flexibility Across Families | Maximum Likelihood Estimation | Basic MLE Workflow | Inference Results | Goodness-of-Fit Assessment | Model Selection | Comparing Nested Models | Interpretation | Advanced Topics | Profile Likelihood | Confidence Regions | Performance Benchmarking | Computational Efficiency | Practical Applications | Example: Modeling Proportions | Recommendations | When to Use Each Distribution | Model Selection Workflow | Conclusion | Further Reading | Session Information

1. Introduction and Preliminaries | 1.1 Motivation and Background | 1.2 Mathematical Preliminaries | 2. The Generalized Kumaraswamy Distribution and Its Subfamilies | 2.1 Definition and Fundamental Properties | 2.2 The Hierarchical Structure | 2.2.1 Beta–Kumaraswamy distribution | 2.2.2 Kumaraswamy–Kumaraswamy distribution | 2.2.3 Exponentiated Kumaraswamy distribution | 2.2.4 McDonald distribution | 2.2.5 Kumaraswamy distribution | 2.2.6 Beta distribution | 3. Likelihood-Based Inference | 3.1 The Log-Likelihood Function | 3.2 Maximum Likelihood Estimation | 3.3 Likelihood Ratio Tests | 4. Analytical Derivatives and Information Matrix | 4.1 The Score Vector | 4.2 The Hessian and Observed Information Matrix | 4.2.1 Diagonal elements | 4.2.2 Off-diagonal elements | 4.3 Asymptotic Variance–Covariance Matrix | 5. Computational Aspects and Discussion | 5.1 Numerical Stability | 5.2 Optimization | 5.3 Gradient Accuracy | 5.4 Practical Recommendations | 5.5 Discussion | References