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I don't have a background in probability, perhaps the following questions are straightforward.

Suppose that $A$ and $B$ are two independent random samples, this two random samples are the output of monte carlo simulation for uncertainty propagation. The $PDF$ is the empirical distribution function, and the $CDF$ is the empirical cumulative distribution function. I plot the $PDF$ and the $CDF$.

  1. Is there any condition on this two samples $A$ and $B$ to write this? $$ PDF(A>B) = PDF(A-B>0) $$ $$ = 1 - CDF_{A-B}(0)$$

  2. How to calculate the empirical $PDF$ of $A-B$ from the empirical $PDF$ of $A$ and the empirical $PDF$ of $B$ ?

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  • $\begingroup$ (1) makes no sense at all. What are you trying to assert? (2) works the same as always: take the convolution of the two PDFs. $\endgroup$ – whuber Jul 25 '17 at 13:59
  • $\begingroup$ I'm looking to define a stochastic order between two empirical random variables by comparing $P(A>B)$. $\endgroup$ – Zayna Jul 28 '17 at 7:23

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