Confidence Interval for Pareto Distribution A random variable is

abitinomaq1 2022-03-25 Answered
Confidence Interval for Pareto Distribution
A random variable is said to have probability density function
fX(x)=αkαxα+1,α,k>0;  and  ;x>k.
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Answers (1)

Tristatex9tw
Answered 2022-03-26 Author has 18 answers

Step 1
k^>x if and only if [X1>x &  & Xn>x]
and the probability of that is (Pr(X1>x))n
Pr(X1>x)=xαkαuα+1,du=(kx)α,
so
Pr(k^>x)=(kx)nα.
Thus,
Pr(x1<k^<x2)=(kx1)nα(kx2)nα.
Pr(Ak<k^<Bk)=AnαBnα.
Pr(A<k^k<B)=
Pr(1B<kk^<1A)=
Pr(k^B<k<k^A)=
This gives you a confidence interval for k if α is known. Since α is not known, there is more work to do. (You have to choose A and B to get you the probablities that you want.)

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