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This is a novice question, which I struggling to answer. I want to find P(A>B) where A and B are random variables from two different distributions. Although two distributions that I have are not classical variants (e.g. normal or binomial etc) but a sampled distribution, I cannot use analytical approach where I could look at the PDF and reason about it, hence I would like to find a numerical solution.

I was wondering if I could use this formula from this answer (Probability that random variable B is greater than random variable A)

\begin{align*} \theta=P(A<B) = \Phi\left(\dfrac{\mu_B-\mu_A}{\sqrt{\sigma_A^2+\sigma_B^2}}\right) \end{align*}

I could easily estimate \begin{align*} (μA,μB,σA,σB) \end{align*}

Are there other solution for it?

kjetil b halvorsen
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kirbo
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    If the data are independent random samples, then look into the [Wilcoxon/Mann Whitney rank sum test](http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test#Effect_Sizes). – whuber Dec 11 '14 at 20:58

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