Stochastic Comparisons of Weighted Distributions and Their Mixtures

Al-Babtain, Abdulhakim A.; Shrahili, Mansour; Alshehri, Mohammed; Kayid, Mohamed

doi:10.3390/e22080843

Cited by 4 publications

(1 citation statement)

References 44 publications

(60 reference statements)

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“…Stochastic comparisons for two finite mixtures using majorization in the sense of the usual stochastic order, the hazard rate order and the reversed hazard rate order have been discussed by Nadeb and Torabi [23]. Albabtain et al [1] have considered a parametric family of weighted distributions and their mixtures and have provided some stochastic comparisons. For some aging properties and stochastic comparisons of mixtures, we refer, among others, to Finkelstein and Esaulova [17], Finkelstein and Esaulova [18], Shaked and Shanthikumar [27] and Misra and Naqvi [22].…”

Section: Introductionmentioning

confidence: 99%

Stochastic properties of generalized finite α-mixtures

Shojaee¹,

Asadi²,

Finkelstein

2021

Prob. Eng. Inf. Sci.

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Most of the real-life populations are heterogeneous and homogeneity is often just a simplifying assumption for the relevant statistical analysis. Mixtures of lifetime distributions that correspond to homogeneous subpopulations were intensively studied in the literature. Various distributional and stochastic properties of finite and continuous mixtures were discussed. In this paper, following recent publications, we develop further a mixture concept in the form of the generalized α-mixtures that include all mixture models that are widely explored in the literature. We study some main stochastic properties of the suggested mixture model, that is, aging and appropriate stochastic comparisons. Some relevant examples and counterexamples are given to illustrate our findings.

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Section: Introductionmentioning

confidence: 99%

Stochastic properties of generalized finite α-mixtures

Shojaee¹,

Asadi²,

Finkelstein

2021

Prob. Eng. Inf. Sci.

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On some stochastic comparisons of arithmetic and geometric mixture models

Shojaee

Babanezhad

2022

Metrika

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Impact of Probabilistic Modeling Alternatives on the Seismic Fragility Analysis of Reinforced Concrete Dual Wall–Frame Buildings towards Resilient Designs

Martinez,

Gallegos,

Araya-Letelier

et al. 2024

Sustainability

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Demands to advance toward more resilient and sustainable cities in terms of reducing casualties, economic losses, downtime, and environmental impacts derived from earthquake-induced damage are becoming more frequent. Indeed, accurate evaluations of the seismic performance of buildings via numerical simulations are crucial for the sustainable development of the built environment. Nevertheless, performance estimations could be influenced by alternative probabilistic methods that can be chosen throughout the procedure of building-specific risk assessment, specifically in the construction and validation of fragility functions. This study evaluates the numerical impacts of selecting different probabilistic models on seismic risk metrics for reinforced concrete dual wall–frame buildings. Specifically, alternative probabilistic models are implemented and evaluated for (i) the identification and elimination of unusual observations within the simulated data (i.e., outliers); (ii) the selection and implementation of different Probability Distribution Functions (PDFs) to estimate fragility functions at different limit states (LSs); and (iii) the application of goodness-of-fit tests and information criteria to assess the validity of proposed PDFs. According to the results, the risk measures showed large variability at the extreme building LS (collapse). On the other hand, for a lower LS (service level), the measures remain similar in all the cases despite the methods selected. Further, the variability observed in the collapse response is up to two times that after eliminating data outliers. Finally, the large variability obtained with the evaluated alternative probabilistic modeling methods suggests re-opening the technical discussion over the state of the practice often used in earthquake engineering to improve the decision-making process, mitigating earthquake-induced consequences in an environmentally, economically, and socially beneficial manner.

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Stochastic Comparisons of Weighted Distributions and Their Mixtures

Cited by 4 publications

References 44 publications

Stochastic properties of generalized finite α-mixtures

Stochastic properties of generalized finite α-mixtures

On some stochastic comparisons of arithmetic and geometric mixture models

Impact of Probabilistic Modeling Alternatives on the Seismic Fragility Analysis of Reinforced Concrete Dual Wall–Frame Buildings towards Resilient Designs

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