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Goodness of fit tests indicate whether or not it is reasonable to assume that a random sample comes from a specific distribution.

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Hypothesis testing if two random variables come from a related underlying function

I'm not sure this is a well-posed problem if the two functions are allowed to be arbitrary. I'm guessing from your notation that you actually know something about the form of $F_1$ and $F_2$ (for inst …
Patrick Coulombe's user avatar