sn_match: Match three cumulants to a skew-normal parameterisation

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Match three cumulants to a skew-normal parameterisation

Description

Inverts the skew-normal moment formulas to convert (mu, sigma, gamma) into (xi, omega, alpha) parameters. Returns NULL with a warning when |gamma| exceeds the skew-normal ceiling (~0.9953) – in that regime the third cumulant cannot be matched by any skew-normal and the caller should fall back to direct-quadrature quantiles.

Usage

sn_match(mu, sigma, gamma)

Arguments

mu	Posterior mean (numeric, length 1).
sigma	Posterior standard deviation (positive numeric, length 1).
gamma	Posterior skewness (numeric, length 1).

Value

Named list with elements xi, omega, alpha; or NULL if |gamma| >= .SN_GAMMA_MAX.

References

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12: 171-178.

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.