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Dear all,

I am currently trying to define the probability density function P(X/Y<y).

I indeed have an n-by-2 matrix where column 1 gives values of X and column 2 gives matrix of Y. They are correlated (coef=0.5).

How can I define the conditional pdf P(X<x/Y<y) from this matrix ?

Thank you for your help!

Best

Laurène

Jeff Miller
on 23 Oct 2019

Maybe start with 'ksdensity' to estimate the joint pdf of x & y from your observed x,y pairs. Once you have a good numerical estimate of the joint density at each (x,y) pair, you should be able to estimate whatever you want from that.

It isn't entirely clear what you want to compute, though, because "conditional pdf P(X<x/Y<y)" looks like a conditional CDF instead of PDF. It might help to give a small numerical example to show what number you would like to get.

Jeff Miller
on 30 Oct 2019

Do you know the exact bivariate long-normal distribution of a and c (i.e., do you know the value of the correlation)?

If so, then you should be able to compute the marginal distribution of a for each particular c.

I don't really understand what you are trying to do, though, so I'm not sure how you could achieve it once you had this marginal distribution.

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