Fisher information in exponential-weighted location-scale distributions

In this article, the comparison between the Fisher information on parameters of the weighted distributions and the parent distributions is done. The most common family of distributions, location-scale family, is considered with the exponential weight function w(x) = e(beta x) where beta is a constant. Conditions under which the weighted distributions are more (less) informative than the parent distribution are given. This was done for location, scale, and location-scale families when the scale parameter is considered as a nuisance parameter. Furthermore, using the transformation technique, we show that the results in location-scale family can be generalized to the broader classes of problems that studied the Fisher information of the weighted distributions such as Tzavelas and Economou (2014). As the exponential weight function can include some other weight functions, the obtained results in this article can be generalized for some other weight functions.