smooth.ADAM.scale

property ADAM.scale: float

Internal optimisation scale of the error distribution (R: adam_obj$scale).

This is the scale parameter the cost function uses inside the density (e.g. for dgnorm it’s the α in f(x; β, σ) = β/(2σ Γ(1/β)) exp(-(|x|/σ)^β)). It coincides with the empirical residual std (sigma) only for the Normal distribution; for non-normal distributions the two differ — sigma is then the variance-adjusted residual std-dev (matches R’s sigma() generic), while scale is the density-parameterising scalar used by the cost function.

Use sigma for reporting “error standard deviation” / constructing intervals; use scale for re-evaluating the likelihood or other quantities defined in terms of the density.