"Weighted empirical distribution", terminology question

I have some weighted simulations of two variables. I would like to have an idea of how they are correlated. An option is to use a bivariate density estimate which allows the weights. Another option is to pick at random the simulations according to their weight, and to graph the scatterplot of this thing:

## 'Sims' is a dataframe containing 5000 weighted simulations of 'x1' and 'x2'
indices <- sample.int(5000, replace = TRUE, prob = the_weights)
result  <- Sims[indices, ]
plot(x2 ~ x1, data = result)


Does this "thing" has a name? Perhaps a sample from the empirical distribution of the simulations, or something like that?

• Why not just using weighted correlation stats.stackexchange.com/questions/221246/… ?
– Tim
Nov 5 '20 at 21:47
• @Tim Sorry, I didn't want to mean I'm interested in some correlation measure. I want to see the "bivariate shape" of the weighted simulations. Nov 5 '20 at 22:09