Some results on ordering of survival functions through uncertainty

Ebrahimi, Nader; Kirmani, S. N. U. A.

doi:10.1016/0167-7152(95)00170-0

Cited by 62 publications

(39 citation statements)

References 9 publications

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“…Here, the last inequality is obtained by noting that hazard rate ordering implies that the residual lifetimes are stochastically ordered and that f * (x)/g(x) is decreasing in x. The proof in the increasing case is similar and is given in Ebrahimi and Kirmani (1996b).…”

Section: Theorem 3 Let F = {F : λ F (T) ≤ R(t)} Be a Compact Set Of mentioning

confidence: 93%

“…Several authors have studied information functions that take age into account (Ebrahimi (1996), Ebrahimi and Kirmani (1996a), (1996b), Di Crescenzo and Longobardi (2002, Minimum dynamic discrimination information models 645 Belzunce et al (2004), Asadi et al (2004)). Consideration of age has led to some important insights about lifetime models, such as an information characterization of the proportional hazards model (Ebrahimi and Kirmani (1996a)) and MDE characterizations of various lifetime models, including some mixture distributions, for which no other maximum entropy formulation is available (Asadi et al (2004)).…”

Section: Introductionmentioning

confidence: 99%

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Minimum dynamic discrimination information models

et al. 2005

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In this paper, we introduce the minimum dynamic discrimination information (MDDI) approach to probability modeling. The MDDI model relative to a given distribution G is that which has least Kullback-Leibler information discrepancy relative to G, among all distributions satisfying some information constraints given in terms of residual moment inequalities, residual moment growth inequalities, or hazard rate growth inequalities. Our results lead to MDDI characterizations of many well-known lifetime models and to the development of some new models. Dynamic information constraints that characterize these models are tabulated. A result for characterizing distributions based on dynamic Rényi information divergence is also given.

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Section: Theorem 3 Let F = {F : λ F (T) ≤ R(t)} Be a Compact Set Of mentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Minimum dynamic discrimination information models

et al. 2005

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“…Several authors have studied the stochastic comparisons. For example, Ebrahimi and Kirmani (1996), Raqab and Amin (1996), Kochar (1999), Abbasnejad and Argami (2011), Di Crescenzo and Longobardi (2013), Psarrakos and Navarro (2013), Gupta et al (2014). We continue this line of researches by exploring some properties of stochastic comparisons based on Tsallis entropy of order statistics.…”

Section: Introductionmentioning

confidence: 99%

Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons

Baratpour¹,

Khammar²

2016

JSRI

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“…The residual entropy has been used to measure the wear and tear of systems and to characterize, classify and order distributions of lifetimes. See Belzunce et al [3], Ebrahimi [4] and Ebrahimi and Kirmani [6]. Di Crescenzo and Longobardi [5] introduced the notion of past entropy and motivated its use in real-life situations.…”

Section: Interval Entropymentioning

confidence: 99%

“…Ebrahimi and Kirmani [6] introduced the residual discrimination measure and studied the minimum discrimination principle. Di Crescenzo and Longobardi [7] have considered the past discrepancy measure and presented a characterization of the proportional reversed hazards model.…”

Section: Introductionmentioning

confidence: 99%

Interval Entropy and Informative Distance

Misagh

Yari

2012

Entropy

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Abstract:The Shannon interval entropy function as a useful dynamic measure of uncertainty for two sided truncated random variables has been proposed in the literature of reliability. In this paper, we show that interval entropy can uniquely determine the distribution function. Furthermore, we propose a measure of discrepancy between two lifetime distributions at the interval of time in base of Kullback-Leibler discrimination information. We study various properties of this measure, including its connection with residual and past measures of discrepancy and interval entropy, and we obtain its upper and lower bounds.

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Some results on ordering of survival functions through uncertainty

Cited by 62 publications

References 9 publications

Minimum dynamic discrimination information models

Minimum dynamic discrimination information models

Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons

Interval Entropy and Informative Distance

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