Follow the proof of Theorem 10.14 to demonstrate that when random sampling from the continuous PDF \(f(z ; \Theta)\) with scalar parameter \(\Theta\),

\(-2 \sum_{i=1}^{n} \ln \left[1-F\left(X_{i} ; \Thetaight)ight] \sim \chi_{2 n}^{2}\)

is a pivotal quantity for \(\Theta\).