Cumulative Residual Entropy of Linear Consecutive $$k$$ k -out-of- $$n$$ n:G Systems and their Applications

M. Kayid () and N. Balakrishnan
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M. Kayid: King Saud University
N. Balakrishnan: McMaster University

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-22

Abstract: Abstract This study provides a detailed investigation into the properties of the cumulative residual entropy of $$k$$ k -out-of-n:G systems with consecutive structure. We first derive a useful formula to compute the cumulative residual entropy of the lifetime of a consecutive $$k$$ k -out-of- $$n:\text{G}$$ n : G system. Based on this formula, we then investigate the cumulative residual entropy of $$k$$ k -out-of-n:G systems with consecutive structure in terms of well-known stochastic orders. We also derive some useful bounds. For practical applications, we introduce two nonparametric estimators of the cumulative residual entropy of consecutive $$k$$ k -out-of- $$n$$ n : G systems. The efficiency and performance of these estimators are demonstrated through the use of simulated datasets, and in addition through an image processing application.

Keywords: Consecutive $$k$$ k -out-of-n:G systems; Cumulative residual entropy; Shannon entropy; Stochastic orders; Image processing (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10176-4

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