Is anybody know a good tutorial about how we calculate Confidence Intervals of not Gaussian functions? I give some example of what I kind of function I think about:
1st example: Let be $ X_1, X_2 \dots X_n $ i.i.d. $ Exp(\lambda) $ random variables, where is $\lambda$ unknown. We observe $ min(X_i) $. I would like to understand, how we calculate the confidence interval for $ \Theta = 1/\lambda$.
2nd. example: Let be $ X_1, X_2 \dots X_n $ i.i.d. $ Uni(0,\Theta) $ random variables, where is $\Theta$ unknown. We observe $ max(X_i) $. I would like to understand, how we calculate the confidence interval $\Theta$.
I am OK, to calculate the CDF of these max, min etc. function, but after this, I do not know how to progress.
My statistic knowledge kind of limited, so I am looking for some explanation where they do not just give a branch of math formula but also they explain in plain English.