Cumulative entropy properties of consecutive systems

Mashael A. Alshehri; Mohamed Kayid; Mashael A. Alshehri; Mohamed Kayid

doi:10.3934/math.20241527

AIMS Mathematics

2024, Volume 9, Issue 11: 31770-31789. doi: 10.3934/math.20241527

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Cumulative entropy properties of consecutive systems

Mashael A. Alshehri ^{1
,
,},
Mohamed Kayid ²

1.
Department of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh, 11362, Saudi Arabia
2.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 21 September 2024 Revised: 30 October 2024 Accepted: 05 November 2024 Published: 07 November 2024
MSC : 94A17

We investigated certain properties of cumulative entropy related to the lifetime of consecutive $ k $-out-of-$ n $:F systems. First, we presented a technique to compute the cumulative entropy of the lifetimes of these systems and studied their preservation properties using the established stochastic orders. Furthermore, we derived valuable bounds applicable in cases where the distribution function of component lifetimes is complex or when systems consist of numerous components. To facilitate practical applications, we introduced two nonparametric estimators for the cumulative entropy of these systems. The efficiency and reliability of these estimators were demonstrated using simulated analysis and subsequently validated using real data sets.
- consecutive $ k $-out-of-$ n $:F systems,
- cumulative entropy,
- Shannon entropy,
- stochastic orders,
- real data
Citation: Mashael A. Alshehri, Mohamed Kayid. Cumulative entropy properties of consecutive systems[J]. AIMS Mathematics, 2024, 9(11): 31770-31789. doi: 10.3934/math.20241527

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Abstract

We investigated certain properties of cumulative entropy related to the lifetime of consecutive $ k $-out-of-$ n $:F systems. First, we presented a technique to compute the cumulative entropy of the lifetimes of these systems and studied their preservation properties using the established stochastic orders. Furthermore, we derived valuable bounds applicable in cases where the distribution function of component lifetimes is complex or when systems consist of numerous components. To facilitate practical applications, we introduced two nonparametric estimators for the cumulative entropy of these systems. The efficiency and reliability of these estimators were demonstrated using simulated analysis and subsequently validated using real data sets.

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