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Homework Help: Finding one sided confidence intervals

  1. Mar 27, 2012 #1
    1. Let X1,...,Xn be iid with cdf Fθ, where Fθ(x) = (x/θ)^β for x in [0, θ]. Here β>0 is a known constant and θ>0 is an unknown parameter. Let X(n)= max (X1,...,Xn). f(x|θ)=nβ(x^(nβ-1))/(θ^(nβ)) when x is in [0, θ].
    Part one was to show that P= X(n)/θ is a pivot for θ. Which I did by showing its distribution doesn't depend on any unknowns.
    Part two is to find the right-sided 95% confidence interval for θ.

    I know to make 1-alpha= Pr(Q(alphaL) ≤ P ≤ Q(alphaU))
    = Pr(X(n)/Q(alphaU) ≤θ≤ X(n)/Q(alphaL))

    But then I'm not sure where to go from there. I know it needs to be in the form of [L(X1,...,Xn), c] where c is some constant. I know I need to make alphaL and alphaU either .05 and 1 or 0 and .95...
    Thanks so much any help would be great, as the next problem builds on this one.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
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