Jensen–Shannon information of the coherent system lifetime

Asadi, Majid; Ebrahimi, Nader; Soofi, Ehsan S.; Zohrevand, Younes

doi:10.1016/j.ress.2016.07.015

Cited by 23 publications

(32 citation statements)

References 32 publications

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“…They also provided expressions for the Kullback-Leibler discrimination information of a mixed system and component lifetimes. Asadi, Ebrahimi, Soofi, and Zohrevand [3] proposed the Jensen-Shannon (JS) information criteria for comparison of mixed systems, which is a scalar function of the signature and ranks systems based on their designs. They proved that the JS information is non-negative and its minimum is attained by r-out-of-n systems.…”

Section: )mentioning

confidence: 99%

On Extropy Properties of Mixed Systems

Qiu¹,

Wang²,

Wang³

2018

Prob. Eng. Inf. Sci.

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An expression of the extropy of a mixed system's lifetime was given firstly. Based on this expression, two mixed systems with same signature but with different components were compared. It was shown that the extropy of lifetime of a mixed system equals to that of its dual system if the lifetimes of the components have symmetric probability density function. Moreover, some bounds of the extropy of lifetimes of mixed systems were obtained and the concept of Jensen–extropy (JE) divergence of mixed systems was proposed. The JE divergence is non-negative and it can be used as an alternative information criteria for comparing mixed systems with homogeneous components. To illustrate the applications of JE divergence, some examples are addressed at the end of this paper.

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Section: )mentioning

confidence: 99%

On Extropy Properties of Mixed Systems

Qiu¹,

Wang²,

Wang³

2018

Prob. Eng. Inf. Sci.

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“…The difference between the two sides of the inequality in gives the Jensen–Shannon (JS) divergence of the mixture error model that has the following representations:

\begin{matrix} J S (f_{ε} : f_{1}, f_{2}, π) & = H (ε) - [π H (ε_{1}) + (1 - π) H (ε_{2})] \\ = π K (f_{1} : f_{ε}) + (1 - π) K (f_{2} : f_{ε}) \geq 0 . \end{matrix}

The inequality becomes equality if and only if f k ( ε )= f ε ( ε ), k =1,2 almost everywhere, implying that there is no outlier. Using and an upper bound for JS given by Asadi et al (), we have the following bounds for the error entropy

π H_{1} + (1 - π) H_{2} \leq H (ε) \leq π H_{1} + (1 - π) H_{2} + π (1 - π) J (f_{1}, f_{2}),

where H k = H ( ε k ), k =1,2 and J ( f 1 , f 2 )= K ( f 1 : f 2 )+ K ( f 2 : f 1 ) is the Jeffreys divergence. Estimates of these bounds can be used to assess presence of outliers.…”

Section: Mixture Modelsmentioning

confidence: 99%

Ranking Forecasts by Stochastic Error Distance, Information and Reliability Measures

Ardakani

Ebrahimi

Soofi

2018

Int Statistical Rev

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The stochastic error distance (SED) introduced by Diebold and Shin (2017) ranks forecast models by divergence between distributions of the errors of the actual and perfect forecast models. The basic SED is defined by the variation distance and provides a representation of the mean absolute error, but by basing ranking on the entire error distribution and divergence, the SED moves beyond the traditional forecast evaluations. First, we establish connections between ranking forecast models by the SED, error entropy and some partial orderings of distributions. Then, we introduce the notion of excess error for forecast errors of magnitudes larger than a tolerance threshold and give the SED representation of the mean excess error (MEE). As a function of the threshold, the MEE is a local risk measure. With the distribution of the absolute error as a prior for the threshold, its Bayes risk is the entropy functional of the survival function, which is a known measure in the information theory and reliability. Notions and results are illustrated using various distributions for the error. The empirical versions of SED, MEE and its Bayes risk are compared with the mean squared error in ranking regression and autoregressive integrated moving average models for forecasting bond risk premia.

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“…They also investigated the discrimination information between the entropy of system's lifetime with the parent distribution as well as the order statistics. In Asadi et al, a useful merge of the information theory and the mixture representation of the system reliability function has been presented. Specifically, they have shown that the Jensen‐Shannon divergence of the mixture distribution provides information criteria for comparing competing systems solely based on the designs of the systems while the common distribution of the i.i.d.…”

Section: Preliminaries and Notationsmentioning

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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Jensen–Shannon information of the coherent system lifetime

Cited by 23 publications

References 32 publications

On Extropy Properties of Mixed Systems

On Extropy Properties of Mixed Systems

Ranking Forecasts by Stochastic Error Distance, Information and Reliability Measures

Some results on information properties of coherent systems

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