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.
Now the model solution says:
Because it's a non-regular case, you can't differentiate it, so the
likelihood is:
L(t) = 1/t^n, 0 < x_i < t, (i=1...n)
which is the same as:
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?
Thank you.
Neeraj.
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