Fazlollah Lak

One of the important theories in Statistics and Probability is Information Theory. Today, the generalization of information criteria has a special place in the topic of probability and reliability. This topic is related to entropy, information compression, image processing, and other related topics. In this thesis, new measures of entropy in fractional and weighted mode are investigated. In the weighted mode based on the cumulative entropy, the weighted generalized cumulative entropy is expressed, and in the fractional version, with the help of fractional equations, the fractional residual cumulative entropy and the generalized fractional cumulative entropy have been investigated as a criterion for evaluating and measuring the efficiency of uncertainty. Next, the properties and characteristics of the dynamic version of these information criteria, including limits, inequalities, random orders, and the effects of linear transformations, are presented. We also study the relationship of these criteria with other reliability indicators such as hazard rate functions, average life span, average remaining life, etc. Finally, the estimators of the mentioned criteria are to be introduced through experimental data .Then,we will express their applications in financial and medical data.