A density of zero is indicated by "." and a density of less than 1/1000, but
greater than zero is indicated by "+". This highlights the non-zero probability
Selecting Independent produces a bivariate distribution where
Pr(X=x, Y=y) = Pr(X=x)Pr(Y= y).
The "X, X+Y" option, which is not a copula, plots the
bivariate distribution of (X, X+Y). This is useful for modeling loss and
ultimate, where X = loss to date and Y = IBNR.
Apply a frequency distribution to the bivariate
"severity" distribution. For example, X and Y could be per claim indemnity and
ALAE. Applying a frequency distribution for the number of claims gives the
bivariate aggregate distribution of indemnity and ALAE.
Frequency distributions can be applied in addition to
the copula dependence structure.
Model shows the bivariate distribution probabilities and a
simple contour plot of the distribution.
References to Wang
Multivariate distributions: Section 4.2
Measures of Correlation, Section 5.
Copulas: Section 6 and 7. (The normal copula is not
available in this example.)
Appendix B, and Table B.1 in particular, gives for
details of each copula.
Wang's Common Monotone copula is called Max here
(after the Frechet bound); the Reverse Monotone is called Min.