A new measure of inaccuracy for record statistics based on extropy

Abstract

We introduce a new measure of inaccuracy based on extropy between distributions of the nth upper (lower) record value and parent random variable and discuss some properties of it. A characterization problem for the proposed extropy inaccuracy measure has been studied. It is also shown that the defined measure of inaccuracy is invariant under scale but not under location transformation. We characterize certain specific lifetime distribution functions. Nonparametric estimators based on the empirical and kernel methods for the proposed measures are also obtained. The performance of estimators is also discussed using a real dataset.

On the dynamic residual measure of inaccuracy based on extropy in order statistics

“…If we consider F as the actual CDF, then G can be interpreted as a reference CDF. For calculating the remaining uncertainty of a system, which has survived up to time t, the measures defined in Equations ( 8)- (10) are not suitable. Qiu and Jia [25] considered a random variable X t = [X − t|X > t], t ≥ 0, and defined the uncertainty of such system based on extropy as:…”

“…Clearly when t = 0, then Equations ( 11)-( 13) reduce, respectively, to Equations ( 8)- (10). In the following, we study some information theoretic measures based on OS using the probability integral transformation and define extropy and relative information measures.…”