CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY—THE NORMAL CASE

In the distribution family with common support and the one side truncated distribution family,Bickle,I.A.Ibragimov and R.Z.Hasminskii proved two important convolution theorems.As to the two-side truncated case,we also proved a convolution theorem,which plays an extraordinary role in the efficency theory.In this paper,we will study another kind of two-side truncated distribution family,and prove a convolution result with normal form.On the basis of this convolution result,a new kind of efficiency concept is given;meanwhile,we will show that MLE is an efficient estimate in this distribution family.