On dynamic mutual information for bivariate lifetimes

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

doi:10.1239/aap/1449859804

Cited by 21 publications

(10 citation statements)

References 29 publications

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“…This measure is also named 'past entropy' of X; it has been investigated in Di Crescenzo and Longobardi [28], Nanda and Paul [29], Kundu et al [30]. Other results and applications of these dynamic information measures can be found in Sachlas and Papaioannou [31], Kundu and Nanda [32], and Ahmadi et al [33].…”

Section: Results On Dynamic Differential Entropiesmentioning

confidence: 99%

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Crescenzo

Gironimo

2018

Mathematics

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We consider a suitable replacement model for random lifetimes, in which at a fixed time an item is replaced by another one having the same age but different lifetime distribution. We focus first on stochastic comparisons between the involved random lifetimes, in order to assess conditions leading to an improvement of the system. Attention is also given to the relative ratio of improvement, which is proposed as a suitable index finalized to measure the goodness of the replacement procedure. Finally, we provide various results on the dynamic differential entropy of the lifetime of the improved system.

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Section: Results On Dynamic Differential Entropiesmentioning

confidence: 99%

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Crescenzo

Gironimo

2018

Mathematics

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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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“…It is symmetric in the arguments and more concentrated around the diagonal. Two spikes are visible at (0, 0) and (1,1). The CIR copula is plotted at three different values of the parameter γ in the other panels of the Figure. For very large γ, the noise is very small with respect to the drift, and the CIR copula closely resembles the Gaussian one.…”

Section: Comparison Of Different Copula Densitiesmentioning

confidence: 99%

“…[22,25,34]). They have found application in many different fields ranging from finance and insurance [12,15], to reliability [1,33], stochastic ordering [36], geophysics [42], neuroscience [2,3,20,23,35,41], statistics [19] and many more.…”

Section: Introductionmentioning

confidence: 99%

A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence

Bibbona

Sacerdote

Torre

2016

Methodol Comput Appl Probab

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This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone spacetime transformations on the copula density is discussed. This provides us a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models. A possible application in neuroscience is sketched as a proof of concept.

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On dynamic mutual information for bivariate lifetimes

Cited by 21 publications

References 29 publications

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Some results on information properties of coherent systems

A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence

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