Say $f(X_1)$, $f(X_2)$, $f(X_3)$, $f(X_4)$ are the empirical marginal PDFs of random variables $X_1$, $X_2$ , $X_3$, $X_4$. Also given is correlation between each pair of variables $X_1$, $X_2$ , $X_3$, $X_4$. Is it possible to obtain the empirical joint PDF of $f(X_1, X_2, X_3, X_4)$?
$\begingroup$
$\endgroup$
3
-
$\begingroup$ How do you define "empirical marginal PDFs"; $\endgroup$– JohnKCommented Jul 9, 2016 at 17:08
-
$\begingroup$ @JohnK I obtained empirical PDFs from an experiment that I conducted $\endgroup$– SpandyieCommented Jul 9, 2016 at 17:11
-
$\begingroup$ not without additional assumptions (eg. multi-variate normality would be sufficient). $\endgroup$– Matthew GunnCommented Jul 9, 2016 at 17:28
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
1
In general, no.
In fact, even if the marginals are normally distributed, the joint distribution could be quite interesting. Here is an one example: Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?.
-
$\begingroup$ @Vimal the marginals of individual variables are definitely not normally distributed, I think it looks somewhat Gamma distributed. $\endgroup$– SpandyieCommented Jul 10, 2016 at 1:09