Get right transformation of a uniform distribution leading to a Pareto one?

Questions
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1

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

2

You should be able to verify that A is the reciprocal of B by:

1/A[v] == B[v] // Simplify (* True *)

The initial “1/” in A is probably an error.