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1) Distribution is a uniform distribution on the interval (Ө, Ө+1)
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.
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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