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I want to get the conditional probability of P(U=u|V=v) or P(X=x|Y=y) using copulas.However, I found that if I use the copulapdf function of Matlab, the result is bigger than 1! I don't know why. any one could help me? thank very much for your help!

the formulas are following: enter image description here

eric
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    Show your code, maybe? My guess is that you're obtaining PDF with copula, not the probability. – Aksakal Apr 14 '14 at 20:30
  • Sorry, what is the different between PDF and probability? I want to know the probability of P(U=u|V=v). Thanks! – eric Apr 14 '14 at 20:45
  • Probability is the area under [PDF](http://en.wikipedia.org/wiki/Probability_density_function). I'm suspecting that you're getting the value of PDF, not the area. That's why you should post your code. – Aksakal Apr 14 '14 at 20:47
  • Sorry, I don't have code. I am just constructing the formulas. Do you mean I can't get the probability of (U=u|V=v) directly. But I can get the probability of (U – eric Apr 14 '14 at 20:59
  • Show us how you construct these formulas. – Aksakal Apr 14 '14 at 21:00
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    may be I know my mistake: If a probability distribution admits a density, then the probability of every one-point set {a} is zero; – eric Apr 14 '14 at 21:13
  • Sorry, do you understand my meaning? – eric Apr 14 '14 at 21:27

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You probably got the problem by now: any probability of a point on real line for continuous distribution is going to be 0. So your denominator in last equation is 0.

Aksakal
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  • Yes, that is my mistake. So should I calculate the probability in an interval instead of one point? – eric Apr 14 '14 at 21:32
  • @eric, you can compute the probability of one point for discrete distributions and discontinuous distributions (in some cases). For continuous, they're all going to be zeros, and only the intervals make a sense. – Aksakal Apr 14 '14 at 21:34
  • Thanks very much for your help! I think I should change the "=" to"". Thanks again! – eric Apr 14 '14 at 21:35