mixle.utils.automatic.detectors.exgaussian module

Exponentially-modified Gaussian (ex-Gaussian) candidate – a Gaussian convolved with an exponential.

The ex-Gaussian X = N(mu, sigma^2) + Exp(rate=lam) is a flexible 3-parameter right-skewed family that DEGENERATES into a Gaussian (as lam -> inf, the exponential component vanishes) and into a pure exponential (as sigma -> 0). That overlap is exactly what makes it dangerous in automatic selection: an honest 3-parameter fit can shadow the simpler builtins on their own data. So the support gate is deliberately TIGHT – it fires only on data whose sample skewness sits strictly inside the ex-Gaussian’s own range (0, 2), away from the symmetric (Gaussian, skew ~ 0) and pure-exponential (skew ~ 2) boundaries – and the BIC carries the full 3-parameter penalty so it never wins by a hair.