## distribution of an mle for the Truncated Exponential Distribution

Hi,

If anyone could help me on the following it would be very much appreciated.

Suppose we have a random sample X1.....Xn for a truncated exponential distribution:

F(x, delta, theta) = 1/theta * e^-(x-delta)/theta

Write down the joint likelihood function of delta and theta and explain why U = deltahat = min{x1,...xn} and V = thetahat = xbar - deltahat are the mle of the parameters. - I've done upto this part, its the next part that I get stuck on!

Find the distribution of U and hence the expectation of U. Now find the expectation of X, then the expectation of Xbar and hence the expectation of V.

Explain why both estimators are only asymptotically unbiased, and suggest modifications which give unbiased estimators of deltatilde and thetatilde.

Thanks.