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.