Mahmoud Afshari

During time, financial institutions have always been exposed to risk. Risk measure is an important and widely used tool that is widely used in quantitative risk management of insurance companies and financial institutions. The purpose of this dissertation is to introduce coherent quantities of variability criteria based on the measure Lr between the probability distribution and its distorsion. One of the special cases is the the cumulative residual entropy of a distribution. In the following, we introduce the two criteria of Tail-based cumulative residual entropy and Shortfall cumulative residual entropy . Using the entropy measure, we can obtain its functional properties in a class of distributions. We also discuss the Gini function, the Tail Gini, and the Shortfall Gini. We examine the Shortfall cumulative residual entropy for some parametric distribtions such as t distribution, Laplas and Logistic and the Shortfall Gini for normal distribution.