Hello, this is a question about the transformation of a uniform distribution leading to a "standard" Pareto one. Here are two formulas A and B (densities) resulting from this transformation:
A[v_] := (1/D[1/u^(1/a), u]) /. u -> 1/v^a
D[1/u^(1/a), u] // InputForm // Print
B[v_] := -(u^(-1 - 1/a)/a) /. u -> 1/v^a
B is correct, while A is not (does not integrate to 1 on [1,Infinity[ ). Why?
Regards, Claude