Let $X_1,...,X_n$ be iid distribution function of $F(x)$. I want to test whether $F$ is exponential, meaning $F(x)=1-exp(-x), x>0$ or Weibull, $F(x)=1-exp(-x^{\theta}), x>0, \theta>0$. For this, I need to find the Most Powerful test for testing hypothesis $H:\theta=1$ vs $K:\theta=\theta_1>1$. A ...