I have to relate 2 variables in a 2D graph, simple. Each point has 2 pdf's associated with it, i.e. point 1 whose coordinate is ($x_1$, $y_1$). $x_1$ say is a normal(10,1) and the $y_1$ is a weibull(a,b).
The question is, how can I visually represent the graph? is there a way to come up with 2 entry uncertainty? with "bands"?
Any ideas? Thanks!
A couple of ideas:
For each point, plot a dot where the point's pdf is maximized. Then plot a closed curve around that point so that the point's pdf has the same value on all the points on the curve and there is a fixed high probability (say, 90%) that the point is inside the curve. This is easy enough to do if $x_1$ and $y_1$ both have normal distributions (the curve is an ellipse), possibly quite a bit harder for other distributions.
Easier to implement: do a Monte Carlo simulation of each point, that is, simulating the pdfs of the two variables, pseudorandomly generate some number of pairs of $(x_1,y_1)$ values (perhaps a few dozen) and plot a single dot at each pair of generated coordinates. The result will be a "cloud" of dots around the most likely location of each point, provided the dots are drawn small enough relative to the density of plotted data.