swastikamohapatra / probability-statistics-assignments Goto Github PK

What exactly is "plug in estimator" in method of moments?

I am unable to solve for Lognormal and Gamma. The first 2 cases work well and I get some optimal parameters. The regression line seems to be a close fit too. But I'm getting an error : Unable to evaluate fn at intial points in parts 3 and 4. I'll include the plots too and send a pull request so you can see what's happening.

I was able to obtain the best estimates in all the three scenarios, and their AIC values don't seem to differ by much. Lognormal seems to be the best fit for the data.

I was able to solve till the third part but I'm facing difficulty from the fourth part onwards. In part 4, I'm not able to obtain a unique value of r. In part 5, I think it cannot be distributed as a poisson random variable because the mean and variance are different.

When we choose the initial point in optim, do we take (1.5,2.2) as given or start from somewhere earlier and hope it converges?