Some aspects of reversed hazard rate and past entropy

Nair, N. Unnikrishnan; Sunoj, S. M.; Rajesh, G.

doi:10.1080/03610926.2019.1659970

Cited by 11 publications

(5 citation statements)

References 21 publications

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“…The uncertainty in distribution of X t , is equivalent to the uncertainty in the in the random variable X (t) . The study of past entropy, which deals with the entropy properties of the distribution of past lifetimes, and its statistical applications have received considerable attention in the literature, as evidenced by works such as Di Crescenzo and Longobardi [17], Nair and Sunoj [18], and Nair and Sunoj [19]. Li and Zhang [20] studied monotonic properties of entropy in order statistics, record values, and weighted distributions in terms of Rényi entropy.…”

Section: Introductionmentioning

confidence: 99%

TRényi’s Entropy for the Past Life Distribution With Application in Inactive Coherent Systems

Kayid¹,

Shrahili²

2023

Preprint

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For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

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Section: Introductionmentioning

confidence: 99%

TRényi’s Entropy for the Past Life Distribution With Application in Inactive Coherent Systems

Kayid¹,

Shrahili²

2023

Preprint

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“…Various aspects and statistical perspectives on past entropy have been treated in the literature, as can be seen in Di Crescenzo and Longobardi [ 4 ], Nair and Sunoj [ 5 ], Loperfido [ 6 ], and Shangari and Chen [ 7 ], as well as in the references used in these papers. In this case, Gupta et al [ 8 ] obtained some results concerning the residual entropy and past entropy for order statistics, as well as presented several relevant stochastic ordering properties.…”

Section: Introductionmentioning

confidence: 99%

On the Uncertainty Properties of the Conditional Distribution of the Past Life Time

Kayid

Shrahili

2023

Entropy

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For a given system observed at time t, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are n components that have all failed at time t. To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time. We explore various analytical results, including expressions, bounds, and order properties, for this measure. Our results provide valuable insight into the predictability of the coherent system’s life-time, which may be useful in a number of practical applications.

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“…The study of entropy for past events and the relevant applications that have arisen have been accomplished by many researchers. The works carried out by Di Crescenzo and Longobardi [6] and Nair and Sunoj [7] have shed light on this topic. The research carried out by Gupta et al [8] on the aspects and use of past entropy for order statistics was helpful in this area.…”

Section: Introductionmentioning

confidence: 99%

Some New Results Involving Past Tsallis Entropy of Order Statistics

Shrahili,

Kayid

2023

Entropy

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This work focuses on exploring the properties of past Tsallis entropy as it applies to order statistics. The relationship between the past Tsallis entropy of an ordered variable in the context of any continuous probability law and the past Tsallis entropy of the ordered variable resulting from a uniform continuous probability law is worked out. For order statistics, this method offers important insights into the characteristics and behavior of the dynamic Tsallis entropy, which is associated with past events. In addition, we investigate how to find a bound for the new dynamic information measure related to the lifetime unit under various conditions and whether it is monotonic with respect to the time when the device is idle. By exploring these properties and also investigating the monotonic behavior of the new dynamic information measure, we contribute to a broader understanding of order statistics and related entropy quantities.

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Some aspects of reversed hazard rate and past entropy

Cited by 11 publications

References 21 publications

TRényi’s Entropy for the Past Life Distribution With Application in Inactive Coherent Systems

TRényi’s Entropy for the Past Life Distribution With Application in Inactive Coherent Systems

On the Uncertainty Properties of the Conditional Distribution of the Past Life Time

Some New Results Involving Past Tsallis Entropy of Order Statistics

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