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On stochastic ordering among extreme shock models 极端冲击模型的随机排序
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-10-28 DOI: 10.1017/s0269964822000328
Sirous Fathi Manesh, Muhyiddin Izadi, Baha-Eldin Khaledi
{"title":"On stochastic ordering among extreme shock models","authors":"Sirous Fathi Manesh, Muhyiddin Izadi, Baha-Eldin Khaledi","doi":"10.1017/s0269964822000328","DOIUrl":"https://doi.org/10.1017/s0269964822000328","url":null,"abstract":"\u0000 In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation49(1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of \u0000 \u0000 \u0000 $mgeq 1$\u0000 \u0000 possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of \u0000 \u0000 \u0000 $m$\u0000 \u0000 sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76064069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PES volume 36 issue 4 Cover and Back matter PES第36卷第4期封面和封底
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-10-01 DOI: 10.1017/s0269964822000390
{"title":"PES volume 36 issue 4 Cover and Back matter","authors":"","doi":"10.1017/s0269964822000390","DOIUrl":"https://doi.org/10.1017/s0269964822000390","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91254895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PES volume 36 issue 4 Cover and Front matter PES第36卷第4期封面和封面问题
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-10-01 DOI: 10.1017/s0269964822000389
{"title":"PES volume 36 issue 4 Cover and Front matter","authors":"","doi":"10.1017/s0269964822000389","DOIUrl":"https://doi.org/10.1017/s0269964822000389","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91014649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extreme Behaviors of the Tail Gini-Type Variability Measures 尾基尼型变异性测量的极端行为
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-09-23 DOI: 10.1017/s0269964822000304
Hong-Jie Sun, Yu Chen
{"title":"Extreme Behaviors of the Tail Gini-Type Variability Measures","authors":"Hong-Jie Sun, Yu Chen","doi":"10.1017/s0269964822000304","DOIUrl":"https://doi.org/10.1017/s0269964822000304","url":null,"abstract":"\u0000 For a bivariate random vector \u0000 \u0000 \u0000 $(X, Y)$\u0000 \u0000 , suppose \u0000 \u0000 \u0000 $X$\u0000 \u0000 is some interesting loss variable and \u0000 \u0000 \u0000 $Y$\u0000 \u0000 is a benchmark variable. This paper proposes a new variability measure called the joint tail-Gini functional, which considers not only the tail event of benchmark variable \u0000 \u0000 \u0000 $Y$\u0000 \u0000 , but also the tail information of \u0000 \u0000 \u0000 $X$\u0000 \u0000 itself. It can be viewed as a class of tail Gini-type variability measures, which also include the recently proposed tail-Gini functional. It is a challenging and interesting task to measure the tail variability of \u0000 \u0000 \u0000 $X$\u0000 \u0000 under some extreme scenarios of the variables by extending the Gini's methodology, and the two tail variability measures can serve such a purpose. We study the asymptotic behaviors of these tail Gini-type variability measures, including tail-Gini and joint tail-Gini functionals. The paper conducts this study under both tail dependent and tail independent cases, which are modeled by copulas with so-called tail order property. Some examples are also shown to illuminate our results. In particular, a generalization of the joint tail-Gini functional is considered to provide a more flexible version.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87532975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures 相干和混合系统若干可靠性类的寿命保存性及其特征
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-09-23 DOI: 10.1017/s0269964822000316
S. Izadkhah, Ebrahim Amini-Seresht, N. Balakrishnan
{"title":"Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures","authors":"S. Izadkhah, Ebrahim Amini-Seresht, N. Balakrishnan","doi":"10.1017/s0269964822000316","DOIUrl":"https://doi.org/10.1017/s0269964822000316","url":null,"abstract":"This paper examines the preservation of several aging classes of lifetime distributions in the formation of coherent and mixed systems with independent and identically distributed (i.i.d.) or identically distributed (i.d.) component lifetimes. The increasing mean inactivity time class and the decreasing mean time to failure class are developed for the lifetime of systems with possibly dependent and i.d. component lifetimes. The increasing likelihood ratio property is also discussed for the lifetime of a coherent system with i.i.d. component lifetimes. We present sufficient conditions satisfied by the signature of a coherent system with i.i.d. components with exponential distribution, under which the decreasing mean remaining lifetime, the increasing mean inactivity time, and the decreasing mean time to failure are all satisfied by the lifetime of the system. Illustrative examples are presented to support the established results.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85520659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nonparametric estimation of some dividend problems in the perturbed compound Poisson model 摄动复合泊松模型中红利问题的非参数估计
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-09-09 DOI: 10.1017/S0269964822000298
Yang Yang, Jiayi Xie, Zhimin Zhang
{"title":"Nonparametric estimation of some dividend problems in the perturbed compound Poisson model","authors":"Yang Yang, Jiayi Xie, Zhimin Zhang","doi":"10.1017/S0269964822000298","DOIUrl":"https://doi.org/10.1017/S0269964822000298","url":null,"abstract":"In this paper, we consider some dividend problems in the perturbed compound Poisson model under a constant barrier dividend strategy. We approximate the expected present value of dividend payments before ruin and the expected discounted penalty function based on the COS method, and construct some nonparametric estimators by using a random sample on claim number and individual claim sizes. Under a large sample size setting, we perform an error analysis of the estimators. We also provide some simulation results to verify the effectiveness of this estimation method when the sample size is finite.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85331422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Relationships between cumulative entropy/extropy, Gini mean difference and probability weighted moments 累积熵/外向性、基尼均值差与概率加权矩的关系
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-08-26 DOI: 10.1017/s026996482200047x
S. Kattumannil, E. Sreedevi, N. Balakrishnan
{"title":"Relationships between cumulative entropy/extropy, Gini mean difference and probability weighted moments","authors":"S. Kattumannil, E. Sreedevi, N. Balakrishnan","doi":"10.1017/s026996482200047x","DOIUrl":"https://doi.org/10.1017/s026996482200047x","url":null,"abstract":"\u0000 In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative past extropy are also established. We then show that several entropy and extropy measures discussed here can be brought into the framework of probability weighted moments, which would facilitate finding estimators of these measures.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73049748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Phase transitions in biased opinion dynamics with 2-choices rule 带有2选择规则的偏见意见动态的相变
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-08-25 DOI: 10.1017/s0269964823000098
Arpan Mukhopadhyay
{"title":"Phase transitions in biased opinion dynamics with 2-choices rule","authors":"Arpan Mukhopadhyay","doi":"10.1017/s0269964823000098","DOIUrl":"https://doi.org/10.1017/s0269964823000098","url":null,"abstract":"\u0000 We consider a model of binary opinion dynamics where one opinion is inherently “superior” than the other, and social agents exhibit a “bias” toward the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability α > 0 irrespective of its current opinion and opinions of other agents. With probability \u0000 \u0000 \u0000 $1-alpha$\u0000 \u0000 , it adopts majority opinion among two randomly sampled neighbors and itself. We are interested in the time it takes for the network to converge to a consensus on the superior alternative. In a complete graph of size n, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as \u0000 \u0000 \u0000 $Theta(n,log n)$\u0000 \u0000 when the bias parameter α is sufficiently high, that is, \u0000 \u0000 \u0000 $alpha gt alpha_c$\u0000 \u0000 where α\u0000 c\u0000 is a threshold parameter that is uniquely characterized. When the bias is low, that is, when \u0000 \u0000 \u0000 $alpha in (0,alpha_c]$\u0000 \u0000 , we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold \u0000 \u0000 \u0000 $p_c(alpha)$\u0000 \u0000 . If this is not the case, then we show that the network takes \u0000 \u0000 \u0000 $Omega(exp(Theta(n)))$\u0000 \u0000 time on average to reach consensus.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78138848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Almost first-order stochastic dominance by distorted expectations 几乎是一阶随机优势的扭曲预期
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-08-12 DOI: 10.1017/s0269964822000250
Jianping Yang, Tian Zhou, Weiwei Zhuang
{"title":"Almost first-order stochastic dominance by distorted expectations","authors":"Jianping Yang, Tian Zhou, Weiwei Zhuang","doi":"10.1017/s0269964822000250","DOIUrl":"https://doi.org/10.1017/s0269964822000250","url":null,"abstract":"Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89806508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal singular dividend control with capital injection and affine penalty payment at ruin 具有资本注入和仿射罚金支付的最优奇异股利控制
IF 1.1 3区 工程技术
Probability in the Engineering and Informational Sciences Pub Date : 2022-08-12 DOI: 10.1017/S0269964822000249
Ran Xu
{"title":"Optimal singular dividend control with capital injection and affine penalty payment at ruin","authors":"Ran Xu","doi":"10.1017/S0269964822000249","DOIUrl":"https://doi.org/10.1017/S0269964822000249","url":null,"abstract":"In this paper, we extend the optimal dividend and capital injection problem with affine penalty at ruin in (Xu, R. & Woo, J.K. (2020). Insurance: Mathematics and Economics 92: 1–16) to the case with singular dividend payments. The asymptotic relationships between our value function to the one with bounded dividend density are studied, which also help to verify that our value function is a viscosity solution to the associated Hamilton–Jacob–Bellman Quasi-Variational Inequality (HJBQVI). We also show that the value function is the smallest viscosity supersolution within certain functional class. A modified comparison principle is proved to guarantee the uniqueness of the value function as the viscosity solution within the same functional class. Finally, a band-type dividend and capital injection strategy is constructed based on four crucial sets; and the optimality of such band-type strategy is proved by using fixed point argument. Numerical examples of the optimal band-type strategies are provided at the end when the claim size follows exponential and gamma distribution, respectively.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88192787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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