Minimum dynamic discrimination information models

Asadi, Majid; Ebrahimi, Nader; Hamedani, G. G.; Soofi, Ehsan S.

doi:10.1017/s0021900200000681

Cited by 9 publications

(12 citation statements)

References 12 publications

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“…The multivariate dynamic information measures developed in [6] set the stage for extending the univariate MDE and MDDI procedures proposed in [1,3] to higher dimensions. This article took the first step in this direction and provided results for developing multivariate models based on partial information formulated in terms of inequality constraints for the hazard gradient.…”

Section: Discussionmentioning

confidence: 99%

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Models Based on Partial Information About Survival and Hazard Gradient

Asadi¹,

Ashrafi²,

Ebrahimi³

et al. 2010

Prob. Eng. Inf. Sci.

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This article develops information optimal models for the joint distribution based on partial information about the survival function or hazard gradient in terms of inequalities. In the class of all distributions that satisfy the partial information, the optimal model is characterized by well-known information criteria. General results relate these information criteria with the upper orthant and the hazard gradient orderings. Applications include information characterizations of the bivariate Farlie-Gumbel-Morgenstern, bivariate Gumbel, and bivariate generalized Gumbel, for which no other information characterization are available. The generalized bivariate Gumbel model is obtained from partial information about the survival function and hazard gradient in terms of marginal hazard rates. Other examples include dynamic information characterizations of the bivariate Lomax and generalized bivariate Gumbel models having marginals that are transformations of exponential such as Pareto, Weibull, and extreme value. Mixtures of bivariate Gumbel and generalized Gumbel are obtained from partial information given in terms of mixtures of the marginal hazard rates.

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Section: Discussionmentioning

confidence: 99%

“…Asadi et al [1,3] considered = {F} for an univariate F subject to the inequality or differential inequality constraints for the hazard rate or inequality constraints for the mean residual lifetime. They characterized numerous univariate distributions as MDDI and MDE models.…”

Section: : the Minimum Mutual Information (Mmi) Model In Defined Inmentioning

confidence: 99%

Models Based on Partial Information About Survival and Hazard Gradient

Asadi¹,

Ashrafi²,

Ebrahimi³

et al. 2010

Prob. Eng. Inf. Sci.

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“…Asadi et al [15] and [16] proposed maximum dynamic entropy (MDE) and minimum dynamic discrimination information (MDDI) procedures, respectively, for developing lifetime models. The MDE and MDDI procedures extend the maximum entropy and minimum discrimination information principles of inference to the cases when the information is given in terms of hazard rate growth inequality, residual moment inequality, or residual moment growth inequality.…”

Section: Other Recent Developmentsmentioning

confidence: 99%

Global and Dynamic Information Measures for Reliability

Ebrahimi

Soofi

2014

Wiley StatsRef: Statistics Reference Online

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In modeling a duration variable, such as the lifetime of an object as it ages, consideration of the age partitions the support of the lifetime distribution progressively and induces truncated distributions for the past and residual lifetimes. Global information measures of the distribution of the entire lifetime do not change with the age, and thus are static. Information measures of the past and residual lifetime distributions are functions of the age, and hence are dynamic. This article presents an overview of the global and dynamic Shannon entropy, Kullback–Leibler information, and mutual information. Examples include information measures for parallel and series systems, proportional hazard, exponential, and Pareto models.

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“…For more information about other applications of Shannon entropy, see Asadi et al, Cover and Thomas, Ebrahimi et al, among others. Dynamic and bivariate versions can be seen in Asadi et al, Chamany and Baratpour, Jomhoori and Yousefzadeh, Navarro et al, and references therein. Another useful measure to obtain the distance between 2 density functions f and g is the Kullback‐Leibler (KL) distance, defined by

K false(f : g false) = \int_{0}^{\infty} f false(x false) normall normalo normalg \frac{f false(x false)}{g false(x false)} d x = - H false(f false) + H false(f, g false),

where

H false(f, g false) = - E_{f} false[normall normalo normalg g false(X false) false]

is known as “Fraser information” (Kent) and is also known as “inaccuracy measure” (Kerridge).…”

Section: Introductionmentioning

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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Minimum dynamic discrimination information models

Cited by 9 publications

References 12 publications

Models Based on Partial Information About Survival and Hazard Gradient

Models Based on Partial Information About Survival and Hazard Gradient

Global and Dynamic Information Measures for Reliability

Some results on information properties of coherent systems

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