mhn 0.1.0

Initial release.

Distribution functions

• dmhn(), pmhn(), qmhn(), and rmhn() provide density, distribution, quantile, and random generation for the Modified Half-Normal (MHN) distribution of Sun, Kong & Pal (2023).
• All four functions are vectorised over both the evaluation argument and the parameters alpha, beta, gamma, following standard R recycling rules.
• A ParamCache reuses the Fox–Wright Psi normalising constant across consecutive elements that share an (alpha, beta, gamma) triple, so grouped inputs are evaluated significantly faster than calling the functions inside an R loop.

Random generation

• rmhn(..., method = "auto") (default) routes each parameter triple to the cheapest provably-correct sampler: closed-form shortcuts for the special cases, Sun et al. (2023, Algorithms 1 and 3) where they win, and the Gao & Wang (2025) Relaxed Transformed Density Rejection (RTDR) sampler elsewhere.
• method = "rtdr" forces RTDR with its uniform 1/e acceptance bound.
• method = "sun" forces Sun Algorithm 1 (gamma > 0, alpha > 1) or Algorithm 3 (gamma <= 0); Sun Algorithm 2 is intentionally not implemented and an unsupported combination triggers a clear error.

CDF and quantile

• pmhn() uses the Sun et al. (2023, Lemma 1b) series in log space, truncated at the Sun et al. (2023, Supplementary Lemma 10(d)) constructive bound K = max(K1, K2); the truncation residual is bounded by the user’s tolerance divided by Psi.
• For gamma < 0 the series uses sign-separated log-sum-exp + log- diff-exp accumulation and a runtime cancellation guard derived from the double-precision precision floor: when the relative cancellation loss would exceed the user’s tolerance, pmhn() falls back to a peak-normalised Boost.Math quadrature (Gauss-Kronrod for alpha >= 1, tanh-sinh for alpha < 1) of the unnormalised density.
• qmhn() inverts pmhn() via boost::math::tools::toms748_solve on the bracket [sqrt(eps), E(X) + 8 sqrt(Var(X))], doubling the upper end as needed.

Summary statistics

• mhn_mean(), mhn_var(), mhn_skewness(), mhn_kurtosis(), and mhn_mode() evaluate the closed-form / recurrence-based expressions from Sun et al. (2023, Lemmas 2 and 3).

Tests and documentation

• testthat suite with > 1,700 expectations covering goodness-of-fit (Kolmogorov-Smirnov), special-case identities, vectorised recycling, NA / NaN propagation, and the Sun / Gao & Wang acceptance bounds.
• vignette("introduction", package = "mhn") walks through every exported function with runnable examples.
• vignette("theory", package = "mhn") is the theoretical companion: it covers the MHN family and its special cases, the Fox–Wright Psi normalising constant, Algorithms 1 and 3 of Sun et al. (2023), the four-region Gao & Wang RTDR construction, and the rmhn(method = "auto") decision tree.
• citation("mhn") returns three bibentry objects: the package, the Sun et al. (2023) paper, and the Gao & Wang (2025) paper.