Likelihood Ratio Test
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Solution Summary
The Likelihood Ratio Test and construction of confidence interval for the parameters of an extreme value distribution are discussed in the solution.
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Solution (a)
We have the joint p.d.f. of order statistics is
=
Define
Then , , ,...,
Now we can write
, , ,...,
Now the joint p.d.f. of is given by,
,
where
= = =
Thus the joint p.d.f. of is given by,
,
where
This shows that are independently distributed with are i.i.d. as exponential distribution with parameter 1/σ.
If , then are i.i.d. as exponential distribution with parameter 1/σ.
Solution (b)
We have the joint p.d.f. of order statistics is
=
Define and
Then we can write
, , ,...,
Now the joint p.d.f. of is given by,
,
where
= = =1
Thus the joint p.d.f. of is given by,
,
where
This shows that are independently distributed with are i.i.d. as ...
Purchase this Solution
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