Estimating parameters using a different method?

Hi, I have a probability distribution which has two parameters **a** and **b**

I re-parametrized the distribution such that the new distribution has two parameters **c** and **d **where

**c**=**a **

but

**d** = 1/**b** - 1

I can easily estimate **a** and **b** but I need to make inferences on **c** and **d**, specially **d** ,

So my question is: If I estimate **b** and use relationship **d**=1/**b** -1 to find out the values of d Is it correct? Is there any information loss?

Also, How can I find the standard errors and confidence intervals of **d** if those exist for **b** ?

Thank you very much.

Re: Estimating parameters using a different method?

Hey arun4.

If you are using the MLE estimator, you can use what is called the invariance principle to estimate parameters that are functions of a particular random variable.

So lets say you use the MLE estimator for b (call it b_hat). Then if you want to get an estimator for d_hat and you use the MLE estimator to get b_hat then d_hat = f(b_hat) = 1/b_hat - 1 and you're done.

There are also ways of generating intervals for these estimators as well and you might want to get a book on statistical inference.

This is only guaranteed as far as I know for the MLE estimator so don't try and use another one like Method of Moments and do the same thing.

Re: Estimating parameters using a different method?