On the dynamic cumulative residual quantile entropy ordering

Some Results on Stochastic Orderings of Generalized Order Statistics and Spacings

“…In particular, the mean residual life order between the normalized spacings of Xand Y -samples is proved in [19]. The purpose of this paper is to generalize some results on order statistics obtained by [26], [27], [19] and [23] to the case of generalized order statistics. The organization of this paper is as follows: In Section 2, we briefly review some concepts that will be used later.…”

“…For a nonnegative random variable X with survival function F, a new dynamic measure of uncertainty, called the dynamic cumulative residual quantile entropy (DCRQE), is proposed in [23] which is defined as follows:…”

“…Also a new stochastic order based on DCRQE function was introduced in [23]. The definition of this order is given in the following.…”

“…In this paper, we follow this idea and try to generalize some ordering results in the literature from ordinary order statistics and their sample spacings to generalized order statistics and the corresponding spacings. A new stochastic order, called dynamic cumulative residual quantile entropy order, is introduced in [23]. some characterizations, closure and reversed closure properties of this new order is also obtained in [23].…”

“…A new stochastic order, called dynamic cumulative residual quantile entropy order, is introduced in [23]. some characterizations, closure and reversed closure properties of this new order is also obtained in [23]. For ordinary order statistics, in [26] and [27] is shown that if the first order statistics has an increasing mean residual life function, then (i) the corresponding sample spacings also have increasing mean residual life functions; (ii) they can be ordered with respect to mean residual life and variance orders; and (iii) the covariance between the successive spacings is nonnegative.…”