help needed with frm, back testing

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hi all, i didnt know where else to post my thread..
i have found this great book where it explains how to perform back testing, however im not sure whether i understand it correctly (comment below)..
i would be very gratefull if someone could draw a small example with real numbers how to perform it.. thank you..

 

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Consider a simple example of one stress scenario, which we define as a probability distribution fstress (*) of the vector of factor returns. We simulate a vector of risk factor returns from the risk model, calling it f (*) , and we also simulate from the scenario distribution, fstress (*). If we assign a probability α of a draw from the scenario distribution occurring, then we can combine the two distributions as in:

fcomb(*) = f (*) , with probability (1 − α) and fstress (*) , with probability α

Data from the combined distribution is generated by drawing a random variable Ui from a Uniform(0,1) distribution. If Ui is smaller than α, then we draw a return from fstress (*) , otherwise
we draw it from f (*) . The combined distribution can easily be generalized to multiple scenarios, each of which has its own pre-assigned probability of occurring.