1) Distribution is a uniform distribution on the interval (Ө, Ө+1)(adsbygoogle = window.adsbygoogle || []).push({});

Show that Ө1 is a consistent estimator of Ө. Ө1=Ῡ -.5

Show that Ө2 is a consistent estimator of Ө. Ө2=Yn – (n/(n+1)).

2) I think the distribution for this one is a uniform distribution on the interval (0, Ө) but I am not 100% sure.

Let Y1, Y2, …, Yn denote a random sample of size n from a power family distribution. Then the method in Section 6.7 imply that Yn=max(Y1, Y2, …, Yn ) has the distribution function of:

0, y<0

Fn(y)= (y/ Ө)^(αn) , 0 ≤ y ≤ Ө

1, y> Ө

Show that Yn is a consistent estimator of Ө.

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# Statistics Estimator Consistency

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