This paper introduces and studies a new uncertainty measure, the cumulative residual interval entropy (CRIE). Defined as the cumulative residual entropy of a doubly truncated (interval) continuous random variable, this measure has several applications when data fall between two points. The CRIE generalizes the cumulative residual entropy proposed by Rao et al. [31] and the dynamic cumulative residual entropy proposed by Asadi and Zohrevand [1]. We establish some properties of the generalized hazard rate and the doubly truncated mean residual lifetime, which are useful for obtaining results for the CRIE. Furthermore, we provide several representations of the CRIE based on reliability measures, covariance, the relevation transform, and increasing transformations. Finally, upper and lower bounds, as well as monotonicity results for the CRIE, are provided.

翻译：本文提出并研究了一种新的不确定性度量——累积剩余区间熵（CRIE）。该度量定义为双截断（区间）连续随机变量的累积剩余熵，在数据位于两点之间时具有多种应用。CRIE推广了Rao等人[31]提出的累积剩余熵以及Asadi和Zohrevand[1]提出的动态累积剩余熵。我们建立了广义失效率与双截断平均剩余寿命的若干性质，这些性质对于推导CRIE的相关结果具有重要作用。此外，我们基于可靠性度量、协方差、重更新变换及递增变换给出了CRIE的多种表示形式。最后，本文提供了CRIE的上下界估计及其单调性结果。