Proof: Pivotal Quantity

Question

Can anyone give me a clue of how to address this theorem?

Suppose that $T$ es a real-valued statistic. Suppose that $Q(t,\theta)$ es a monotone function of $t$ for each value of $\theta\in \Theta$. Show that if the pdf of $T$, $f(t|\theta)$, cab be expressed in the form

\begin{equation} f(t|\theta)=g(Q(t, \theta))\left|\frac{d}{dt}Q(t,\theta)\right| \end{equation} for some function $g$, then $Q(t,\theta)$ is a pivot.

I know it is also useful to use the change of variable theorem, but i do not see how

Answer 1

The Answer to this question is here: Proof: Pivotal Quantity, in the Cross Validated community