Scope | The MHN($\alpha$, $\beta$, $\gamma$) family | Shape and moments | The Fox–Wright $\Psi$ normalising constant | Sampling: Sun et al. (2023) | Algorithm 1 — $\gamma > 0$, $\alpha > 1$ | Algorithm 3 — $\gamma \leq 0$ | Why Algorithm 2 is not implemented | Sampling: Gao & Wang (2025) RTDR | $T_{c}$-concavity | Working on the log axis when $\alpha < 1$ | The four regions | Why "relaxed" | The rmhn(method = "auto") dispatch | References | Appendix A. Numerical details | A.1 Special cases and their neighbourhoods | A.2 Moments and mode | A.3 Evaluating $\Psi$ | A.4 Density, distribution and quantile functions | Shared by the three functions | Density | Distribution function | Quantile function | A.5 Random generation at extreme parameters | A.6 Timings behind method = "auto" | Appendix B. Misprints in the source papers | B.1 Sun et al. (2023) | B.2 Gao & Wang (2025)

The MHN distribution | Density: dmhn() | Distribution function: pmhn() | Quantile function: qmhn() | Random generation: rmhn() | Moments and mode | Special cases | Further reading | References

Introduction | Comparison with ordinal::clm() | Installation | Quick Start | For ordinal::clm() Users | API Correspondence | Example Comparison | Key Differences | Link Functions | Standard Links (5) | Flexible Links (6) | Link Function Summary | Threshold Structures | Flexible (Default) | Equidistant | Symmetric | Prior Specification | Default Priors | Using prior() Function (Recommended) | Available Distributions | Prior Classes | Legacy API (clm_prior) | Interpreting Results | Basic Methods | Diagnostic Plots | Convergence Diagnostics | Prediction | Category Prediction | Probability Prediction | Posterior Predictive Distribution | Model Comparison | Practical Workflow | Troubleshooting | CmdStan Not Found | Convergence Issues | Divergent Transitions | Memory Issues | References and Resources | Package Resources | Related Packages | Statistical References