Suppose that n 5 observations are taken from the uniform pdf

Suppose that n= 5 observations are taken from the uniform pdf, Hat Theta 2 = 6*Ymin. Which estimator would be better to use? Hat Theta 1= 6/5*Ymax and Theta are Theta is unknown. Two unbiased estimators for fy (y;Theta )= 1/Theta , 0

Solution

The second estimator would be better to use.

As y max can extend upto infinity

But y minimum is 0 hence theta 2 will be near 0.