Let be a random sample from exponential distribution with parameter that is for and .

Find the Uniformly Minimum Variance Unbiased Estimator for where is a known positive constant.

please help me on this. thank you.

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- May 1st 2009, 01:07 AMKat-Mstatistics help needed
Let be a random sample from exponential distribution with parameter that is for and .

Find the Uniformly Minimum Variance Unbiased Estimator for where is a known positive constant.

please help me on this. thank you. - May 1st 2009, 08:34 PMmatheagle
The suff stat for q is the sum, .

Next we need to find a function of this sum that's unbiased for .

Since each , we have . - May 1st 2009, 10:11 PMKat-M
Would you help a little more?

How does knowing that ~ help me figure out the Uniformly Minimum Variance Estimator? - May 1st 2009, 10:34 PMmatheagle
You will need to do the Rao-Blackwell Theorem directly.

Compute - May 1st 2009, 10:42 PMKat-M
i am sorry to ask you this but what is ? Is a funtion?

- May 1st 2009, 10:54 PMmatheagle
- May 2nd 2009, 01:57 AMKat-M
i thought about this for a long time but still i am not sure how to compute .

X1 is part of S. and i dont know how it affects in computing .

i got So when i integrate it from 0 to c, i got . did i do it right? - May 2nd 2009, 02:03 PMmatheagle
Back to where s>c.

We need the density , where .

The density of is .

While and

Noting that we have

Thus

which gives me , which doesn't make sense when n=1. - May 3rd 2009, 07:45 PMmatheagle