Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables

Zhang, Miaomiao; Lü, Bin; Yan, Rongfang

doi:10.3934/math.2021036

Cited by 8 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, in the context of the proportional hazard rate (PHR) model for the case where λ is a random variable (frailty), Gupta and Kirmani [8] and subsequently Xu and Li [9] identified some stochastic ordering properties of the model. The PHR model has attracted the attention of many researchers in applied probability and statistics, for instance, see Psarrakos and Sordo [10], Sankaran and Kumar [11], Zhang et al [12], Arnold et al [13] and Kochar [14]. Considering the proportional reversed hazard rates (PRHR) model, Di Crescenzo [15] made some stochastic comparisons between two candidate distributions of the model that differ in their parameters.…”

Section: Introductionmentioning

confidence: 99%

Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

Shrahili,

Kayid,

Mesfioui

2023

Mathematics

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In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained. Numerical simulation studies have also been provided to examine the examples presented.

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Section: Introductionmentioning

confidence: 99%

Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

Shrahili,

Kayid,

Mesfioui

2023

Mathematics

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“…Panja et al [29] investigated the usual stochastic and hazard rate orderings on series and parallel systems with dependent and heterogeneous components. For more relevant research the reliability of systems with dependent components, one can refer to the works in [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks

Jiao

Yan

2021

Symmetry

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To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.

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Ordering results between extreme order statistics in models with dependence defined by Archimedean [survival] copulas

2022

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Ordering results of extreme order statistics from dependent and heterogeneous modified proportional (reversed) hazard variables

Cited by 8 publications

References 22 publications

Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks

Ordering results between extreme order statistics in models with dependence defined by Archimedean [survival] copulas

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