This paper introduces the dynamic weighted cumulative residual extropy criterion as a generalization of the weighted cumulative residual extropy criterion. The relationship of the proposed criterion with reliability criteria such as weighted mean residual lifetime, hazard rate function, and second-order conditional moment are studied. Also, characterization properties, upper and lower bounds, inequalities, and stochastic orders based on dynamic weighted cumulative residual extropy and the effect of linear transformation on it will be presented. Then, a non-parametric estimator based on the empirical method for the introduced criterion is given, and its asymptotic properties are studied. Finally, an application of the dynamic weighted cumulative residual extropy in selecting the appropriate data distribution on a real data set is discussed.

The Burr Type III distribution‎, ‎also known as the Singh-Maddala distribution‎, ‎is a versatile probability distribution widely used in various fields such as hydrology‎, ‎finance‎, ‎reliability engineering‎, ‎and actuarial science‎. ‎This paper explores the Burr Type III distribution‎, ‎discussing its properties‎, ‎moment calculations‎, ‎stochastic orders‎, ‎and entropy measures tailored for this distribution.