On Mon, 25 Dec 2000 11:27:11 +0000, Neeraj Nagarkatti
<[EMAIL PROTECTED]> wrote:
>Question:
>Let X_1,...,X_n be a random sample from the Uniform U[0,t] distribution,
>i.e. with pdf:
>f(x|t) = 1/t (0 < x < t).
>Obtain the maximum likelihood estimator of t.
>
>L(t) = 1/t^n, 0 < max(X_i) < t.
>And clearly:
>^
>t = max(X_i).
>Now I don't quite understand why the mle has to be the sample maximum.
>Can any1 shed any light as to why this is the case?
If t is less than max(X_i) then the likelihood is zero (since you
would have achieved a result outside the sample space)
If t is more than max(X_i) then L(t) = 1/t^n < 1/max(X_i)^n so it is
not the maximum possible.
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