I computed the kernel estimators for the copula density for two random variables using:
library(kdecopula)
kde.fit <- kdecop(u)
As the values of density can be greater than one I was wondering if I can normalized values by the maximum magnitude and call it normalized joint probability density?
Here is the bivariate copula density and the normalized bivariate copula density
Normalized bivarite copula density:
Thanks in advance for any helps.
Best Answer
In literature, normalization means integrating to $1$, not having a max value equal to $1$. So, joint or univariate densities are already normalized. For the nomenclature, for the function you have, I think max-normalized joint density would be a better name for it.
However, what you do is just scaling your joint PDF so that it hits $1$ at its maximum. Since both in your new function and the original density, these values can't be associated with probabilities, I see no use in doing so. It's not as much different as than multiplying your density with e.g. $5$.