On dynamic mutual information for bivariate lifetimes

Ahmadi, Jafar; Crescenzo, Antonio Di; Longobardi, Maria

doi:10.1017/s0001867800049053

Cited by 3 publications

(2 citation statements)

References 28 publications

(24 reference statements)

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“…It is a special case of a Ali‐Mikhail‐Haq copula. See for instance, Ahmadi et al, where it has been used in the analysis of the mutual information of random lifetimes. For the system lifetime T 1 , recalling the structure given in Table , n. 12, from , and , we have

{\bar{F}}_{T_{1}} (t) = 1 - {[1 - Ĉ (\bar{F} (t), \bar{F} (t))]}^{2} = 1 - {[1 - \frac{\bar{F} (t)}{2 - \bar{F} (t)}]}^{2} = ψ_{1} (\bar{F} (t)),

where

ψ_{1} (v) = 1 - {[1 - \frac{v}{2 - v}]}^{2}, 0 < v < 1 .

The CDF of V 1 = F ( T 1 ) is

G_{V_{1}} false(v false) = 1 - ψ_{1} false(1 - v false)

, and hence, we get

g_{V_{1}} false(v false) = ψ_{1}^{'} false(1 - v false) = 8 v {false(1 + v false)}^{- 3}

, 0< v <1.…”

Section: Systems With Dependent Componentsmentioning

confidence: 99%

Some results on information properties of coherent systems

Toomaj

Crescenzo

Doostparast

2017

Appl Stoch Models Bus & Ind

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Mathematics Subject Classification: 62N05; 94A17This paper considers information properties of coherent systems when component lifetimes are independent and identically distributed. Some results on the entropy of coherent systems in terms of ordering properties of component distributions are proposed. Moreover, various sufficient conditions are given under which the entropy order among systems as well as the corresponding dual systems hold. Specifically, it is proved that under some conditions, the entropy order among component lifetimes is preserved under coherent system formations.The findings are based on system signatures as a useful measure from comparison purposes. Furthermore, some results on the system's entropy are derived when lifetimes of components are dependent and identically distributed. Several illustrative examples are also given.

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{\bar{F}}_{T_{1}} (t) = 1 - {[1 - Ĉ (\bar{F} (t), \bar{F} (t))]}^{2} = 1 - {[1 - \frac{\bar{F} (t)}{2 - \bar{F} (t)}]}^{2} = ψ_{1} (\bar{F} (t)),

where

ψ_{1} (v) = 1 - {[1 - \frac{v}{2 - v}]}^{2}, 0 < v < 1 .

The CDF of V 1 = F ( T 1 ) is

G_{V_{1}} false(v false) = 1 - ψ_{1} false(1 - v false)

, and hence, we get

g_{V_{1}} false(v false) = ψ_{1}^{'} false(1 - v false) = 8 v {false(1 + v false)}^{- 3}

, 0< v <1.…”

Section: Systems With Dependent Componentsmentioning

confidence: 99%

Some results on information properties of coherent systems

Toomaj

Crescenzo

Doostparast

2017

Appl Stoch Models Bus & Ind

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“…The topic of measuring the information content for bivariate (multivariate) distributions when their supports are truncated progressively are considered in recent past. Some important results in this area have been provided in Ebrahimi et al (2007), Navarro et al (2011Navarro et al ( , 2014, Sunoj and Linu (2012), Rajesh et al (2014), Kundu and Kundu (2017), Ahmadi et al (2015) and the references therein. In this section we confine our study to extend CRI defined in (1.5) to the bivariate setup.…”

Section: Definition and Properties Of Bivariate And Conditional Cri For (X I |X J > T J )mentioning

confidence: 99%

Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Ghosh

Kundu

2017

Stat Papers

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In a recent paper, Kundu et al. (Metrika 79:335-356, 2016) study the notion of cumulative residual inaccuracy (CRI) and cumulative past inaccuracy (CPI) measures in univariate setup as a generalization of cumulative residual entropy and cumulative past entropy, respectively. Here we address the question of extending the definition of CRI (CPI) to bivariate setup and study their properties. We also prolong these measures to conditionally specified models of two components having possibly different ages or failed at different time instants called conditional CRI (CCRI) and conditional CPI (CCPI), respectively. We provide some bounds on using usual stochastic order and investigate several properties of CCRI (CCPI) including the effect of linear transformation. Moreover, we characterize some bivariate distributions. KeywordsCumulative residual (past) inaccuracy • Conditionally specified model • Conditional proportional (reversed) hazard rate • Usual stochastic order

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On some dynamic generalized measures of information for conditionally specified models in past life

Ghosh

Kundu

2017

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On dynamic mutual information for bivariate lifetimes

Cited by 3 publications

References 28 publications

Some results on information properties of coherent systems

Some results on information properties of coherent systems

Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

On some dynamic generalized measures of information for conditionally specified models in past life

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