Suppose $X_1,...,X_n$ is a random sample from the distribution with c.d.f. $$F(x;a,b)= 1 - (a/x)^b, \hskip20pt x\geq a, a > 0, b > 0$$ Find the M.L. estimators of $a$ and $b$.
I tried differentiating with respect to a and b to get the p.d.f but this turned out ugly and I don't think I need to use a numerical method to solve for the M.L.E. of each.. Should I be applying a similar method to that used to get the MLE of a uniform distribution.. or is there something I'm not seeing.