model_bivariate

model_bivariate(
    marginal_x,
    marginal_y,
    copula='Normal',
    estimation_method='InferenceFromMargins',
    parameters=None,
    parameter_values=None,
    use_default_flat_priors=None,
)

Two fixed univariate marginals coupled by a bivariate copula.

Parameters

Name	Type	Description	Default
marginal_x	dict	Each a mapping with "family", "data", and "parameter_values" keys describing a fixed marginal.	required
marginal_y	dict	Each a mapping with "family", "data", and "parameter_values" keys describing a fixed marginal.	required
copula	str	One of Normal, StudentT, Clayton, Frank, Gumbel, Joe, or AliMikhailHaq.	"Normal"
estimation_method	str	One of InferenceFromMargins, PseudoLikelihood, or FullLikelihood.	"InferenceFromMargins"
parameters		As in :func:model_univariate.	None
parameter_values		As in :func:model_univariate.	None
use_default_flat_priors		As in :func:model_univariate.	None

Returns

Name	Type	Description
	Model	The assembled model spec.

Notes

Fit an Archimedean copula (Clayton, Frank, Gumbel, Joe, AliMikhailHaq) with optimizer="DifferentialEvolution". :func:fit_mle and :func:fit_map default to "NelderMead", whose start point is the midpoint of the copula’s constraint range: for Gumbel, whose range is {1, 100}, that is theta 50.5, and the local search slides to the lower bound and reports Success with the independence copula. On 150 Gumbel pairs simulated at theta 3, "NelderMead" returned theta 1.0000 with a log-likelihood of 0.0000 while "DifferentialEvolution" returned theta 3.0334 at 110.5081. "Powell" errors on some samples, so "DifferentialEvolution" is the recommendation rather than any global optimizer. Elliptical copulas (Normal, StudentT) are not affected.