Controls and parameter domains

Main controls

Keyword	Typical values	Purpose
family_set	:default, :all, tuple	candidate pair families
pair_method	:mle	pair-parameter fitting method
selection_criterion	:loglik, :aic, :bic	family score
allow_rotations	true, false	search rotated families
preselect	true, false	prune incompatible rotations
include_independence	true, false	include independence as a candidate
tree_criterion	:tau, :rho	structure weights
tree_algorithm	:kruskal	maximum spanning tree algorithm
trunc	integer	maximum fitted tree
threshold	nonnegative real	weak-dependence independence rule
strict	true, false	rethrow candidate-fit failures instead of skipping failed candidates
trace	true, false	print candidate-level fitting diagnostics

Selection parameter domains

For the default family set, some automatic-selection fits use finite domains matching vinecopulib. This makes AIC/BIC comparisons and external correctness tests meaningful because both engines optimize over the same candidate model space.

Family	Selection domain
Gaussian
Student-t	,
Clayton
Frank
Gumbel
Joe
BB1	,
BB6	,
BB7	,
BB8	,

The strict inequalities reflect the implementation's use of interior points. Boundary values often reduce a BB family to a simpler family and are already represented elsewhere in the candidate set.

These bounds do not change the public copulas

The bounds above apply to automatic vine selection only. Direct construction and direct Copulas.jl fitting keep the mathematical domains defined by Copulas.jl.

For example, bivariate Clayton in Copulas.jl also supports negative parameters. Vine selection instead uses positive Clayton plus 90/270 degree rotations because that is the conventional vinecopulib candidate parameterization.

Likewise, Copulas.jl permits Student-t degrees of freedom outside the selection interval, and direct Frank construction is not redefined by the selector's finite search interval. These are model-selection compatibility choices, not new mathematical domains for the underlying copulas.