Varian [17], Zellner [18], and Basu and Ebrahimi [2] introduced the asymmetric loss function known as Linex (linear exponential) loss function and provided the good estimators for the scale parameters of exponential and normal distributions. Bell [3] considered the Bessel�s and modified function for estimation of variance in normal distribution under life testing problems. In this paper, the improved estimators for the normal and exponential distributions are obtained and using modified version of Bessel�s function it is shown that the existing estimators under mean square criterion are inadmissible.

linex loss function, Bessel function, mean square error (MSE).