constructs validated response-family definitions for generalized mixed models.
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A family definition contains normalized log density, support, variance, link, derivatives, mean semantics, simulation metadata, and dispersion parameterization.
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NegativeBinomial2 uses Size equal to glmmTMB theta and reciprocal to the common statsmodels alpha convention.
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ZeroInflatedFamily and HurdleFamily wrap supported count families and preserve normalized likelihoods.
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Invalid mixture probabilities, nonpositive dispersion parameters, and unsupported links return Failure rather than silently changing family.