It is a well-known result (which can be traced back to Gauss) that the only translation family of probability densities on for which the arithmetic mean is a maximum likelihood estimate of the translation parameter originates from the normal density. We generalize this characterization of the...

A classic result in probability theory states that two independent real-valued random variables having independent sum and difference are either constant or normally distributed with the same variance. In this article conditions are round on independent random variables X and Y taking values in...