COPULA Procedure

Exact Maximum Likelihood Estimation (MLE)

Suppose that the marginal distributions of vector elements x x Subscript i Baseline equals left-parenthesis x Subscript i Baseline 1 Baseline comma x Subscript i Baseline 2 Baseline comma ellipsis comma x Subscript i m Baseline right-parenthesis Superscript down-tack, i equals 1 comma ellipsis comma n are already known to be uniform. Then the parameter theta is estimated by exact maximum likelihood:

ModifyingAbove theta With caret equals arg max Underscript theta element-of normal upper Theta Endscripts sigma-summation Underscript i equals 1 Overscript n Endscripts log c left-parenthesis x Subscript i Baseline 1 Baseline comma x Subscript i Baseline 2 Baseline comma ellipsis comma x Subscript i m Baseline semicolon theta right-parenthesis
Last updated: June 19, 2025