Mahmoud Afshari

In this thesis, we introduce and examined an alternative measure of uncertainty of random variable which called cumulative residual extropy and studied its results and applications. Extropy as the opposite point of entropy and in the other words, a complementary function to the extropy function is introduced. First, examine its characteristics and we have identified inequalities related to CREX and also, examined the relationship between CREX and extropy. Then we examined some of the propertis of stochastic orders and order statistics in relationship to this measure. Some properties of the CREX measure, such as its estimation and applications, are studied. Then, we used some numerical examples to better illustrating of the said sections.