Some results on the proportional reversed hazards model

Crescenzo, Antonio Di

doi:10.1016/s0167-7152(00)00127-9

Cited by 101 publications

(51 citation statements)

References 6 publications

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“…Block et al [4], Di Crescenzo [10], Gupta and Nanda [17], Kijima and Ohnishi [19], and the references therein. For the random lifetime X, we define…”

Section: Background and Preliminary Resultsmentioning

confidence: 99%

“…For more details on the applications and properties of the proportional hazard rate model see e.g. [10], [15], [16], [26] and [27], among others.…”

Section: Definitionmentioning

confidence: 99%

“…. , m, and Y satisfy the proportional hazard rate model with proportionality constant θ, as in (10). By means of some calculations, from (11) we obtain the survival function of X 1:m (Y ), which is expressed as a generalized mixture:Ḡ…”

Section: Proposition 4 Under the Proportional Hazards Rate Model (10)mentioning

confidence: 99%

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Extension of the past lifetime and its connection to the cumulative entropy

Crescenzo

Toomaj

2015

J. Appl. Probab.

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Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and series systems under suitably proportionality assumptions on the hazards rates. Furthermore, we prove that the (reversed) relevation transform is commutative if and only if the proportional (reversed) hazard rate model holds. By repeated application of the reversed relevation transform we construct a decreasing sequence of random variables which leads to new weighted probability densities. We obtain various relations involving ageing notions and stochastic orders. We also exploit the connection of such a sequence to the cumulative entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative formulae for computing the mean and the cumulative entropy of the random variables of the sequence are finally investigated.

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“…Block et al [4], Di Crescenzo [10], Gupta and Nanda [17], Kijima and Ohnishi [19], and the references therein. For the random lifetime X, we define…”

Section: Background and Preliminary Resultsmentioning

confidence: 99%

“…For more details on the applications and properties of the proportional hazard rate model see e.g. [10], [15], [16], [26] and [27], among others.…”

Section: Definitionmentioning

confidence: 99%

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Extension of the past lifetime and its connection to the cumulative entropy

Crescenzo

Toomaj

2015

J. Appl. Probab.

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“…The PRHRM model is flexible enough to accommodate both monotonic and non-monotonic failure rates even though the baseline failure rate is monotonic. See Sengupta et al [26], Di Crescenzo [6] or Gupta and Gupta [11] for some results on this model. For more properties and applications of the geometric vitality function, one may refer to Nair and Rajesh [22].…”

Section: Theorem 22 If the Hazard Rate Functionmentioning

confidence: 99%

Characterizations based on length-biased weighted measure of inaccuracy for truncated random variables

Kundu

2014

Appl Math

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“…See Gupta et al (1998), Di Crescenzo (2000, and Di Crescenzo and Longobardi (2004) for this model and its connection to divergence measures. …”

Section: Which By a Change Of Variable Y = F (X)/f (T) Is Equal Tomentioning

confidence: 99%

Generalized Measures of Divergence in Survival Analysis and Reliability

Vonta

Karagrigoriou

2010

J. Appl. Probab.

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Measures of divergence or discrepancy are used either to measure mutual information concerning two variables or to construct model selection criteria. In this paper we focus on divergence measures that are based on a class of measures known as Csiszár's divergence measures. In particular, we propose a measure of divergence between residual lives of two items that have both survived up to some time t as well as a measure of divergence between past lives, both based on Csiszár's class of measures. Furthermore, we derive properties of these measures and provide examples based on the Cox model and frailty or transformation model.

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Some results on the proportional reversed hazards model

Cited by 101 publications

References 6 publications

Extension of the past lifetime and its connection to the cumulative entropy

Extension of the past lifetime and its connection to the cumulative entropy

Characterizations based on length-biased weighted measure of inaccuracy for truncated random variables

Generalized Measures of Divergence in Survival Analysis and Reliability

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