Question    :  The R Script  “weibull.R” has a walkthrough on three esti- mation methods namely maximum likelihood estimation (MLE), Bayesian regression and graphical method on Weibull distributed data. By replicating the work provided by the provided R Script, provide a proper analysis with codes (either on a Word Documents/PDF document/Markdown and other tools).

1. Generate two sets of simulated data using exponential distribution (which is not going to use again afterward) and Weibull distribution, examine their validity by checking their sample mean and variance (for example, E(XWeibull ) = λΓ(1 + 1/k) for f(x) =  ( )k − 1 exp(x/λ)k ).

2. Fit the models with the methods shown in“weibull.R”using simulated Weibull and Weibull regression models.

3. Fit the same set of data as above with MLE method and Bayesian regression but using exponential regression model.

4. Provide the parameter estimates from the above fitted models (five in total) in a table and comment on its accuracy.

5. Write a short summary in a few sentences(fewer than 5) on Akaike information criterion (AIC; Akaike 1974) and leave-one-out information criterion (looic; Vehtari et al. 2017).  And comment on the goodness- of-fit of the Weibull/exponential models.