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Copula

A function that joins univariate distribution functions to form multivariate distribution functions. A 2-D copula is a function $C:I^2\to I$ such that

\begin{displaymath}
C(0,t)=C(t,0)=0
\end{displaymath}

and

\begin{displaymath}
C(1,t)=C(t,1)=t
\end{displaymath}

for all $t\in I$, and

\begin{displaymath}
C(u_2, v_2)-C(u_1, v_2)-C(u_2,v_1)+C(u_1, v_1)\geq 0
\end{displaymath}

for all $u_1, u_2, v_1, v_2\in I$ such that $u_1\leq u_2$ and $v_1\leq v_2.$

See also Sklar's Theorem




© 1996-9 Eric W. Weisstein
1999-05-25