Abstract Layer reinsurance treaty is a common form obtained in the problem of optimal reinsurance design. In this paper, we study allocations of policy limits in layer reinsurance treaties with dependent risks. We investigate the effects of orderings and heterogeneity among policy limits on the expected utility functions of the terminal wealth from the viewpoint of risk-averse insurers faced with right tail weakly stochastic arrangement increasing losses. Orderings on optimal allocations are presented for normal layer reinsurance contracts under certain conditions. Parallel studies are also conducted for randomized layer reinsurance contracts. As a special case, the worst allocations of policy limits are also identified when the exact dependence structure among the losses is unknown. Numerical examples are presented to shed light on the theoretical findings.
{"title":"Optimal allocation of policy limits in layer reinsurance treaties","authors":"Chuchu Wang, Wei Wang, Yiying Zhang, Peng-fei Zhao","doi":"10.1017/S0269964822000432","DOIUrl":"https://doi.org/10.1017/S0269964822000432","url":null,"abstract":"Abstract Layer reinsurance treaty is a common form obtained in the problem of optimal reinsurance design. In this paper, we study allocations of policy limits in layer reinsurance treaties with dependent risks. We investigate the effects of orderings and heterogeneity among policy limits on the expected utility functions of the terminal wealth from the viewpoint of risk-averse insurers faced with right tail weakly stochastic arrangement increasing losses. Orderings on optimal allocations are presented for normal layer reinsurance contracts under certain conditions. Parallel studies are also conducted for randomized layer reinsurance contracts. As a special case, the worst allocations of policy limits are also identified when the exact dependence structure among the losses is unknown. Numerical examples are presented to shed light on the theoretical findings.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"89 1","pages":"546 - 566"},"PeriodicalIF":1.1,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77205235","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}
Pub Date : 2022-11-22DOI: 10.1017/S0269964821000486
Abedin Haidari, M. Sattari, G. Barmalzan
In this paper, we identify some conditions to compare the largest order statistics from resilience-scale models with reduced scale parameters in the sense of mean residual life order. As an example of the established result, the exponentiated generalized gamma distribution is examined. Also, for the special case of the scale model, power-generalized Weibull and half-normal distributions are investigated.
{"title":"Mean residual life order among largest order statistics arising from resilience-scale models with reduced scale parameters","authors":"Abedin Haidari, M. Sattari, G. Barmalzan","doi":"10.1017/S0269964821000486","DOIUrl":"https://doi.org/10.1017/S0269964821000486","url":null,"abstract":"In this paper, we identify some conditions to compare the largest order statistics from resilience-scale models with reduced scale parameters in the sense of mean residual life order. As an example of the established result, the exponentiated generalized gamma distribution is examined. Also, for the special case of the scale model, power-generalized Weibull and half-normal distributions are investigated.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"225 1","pages":"72 - 85"},"PeriodicalIF":1.1,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76088971","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}
Pub Date : 2022-11-21DOI: 10.1017/s0269964822000419
Liuling Luo, Xingchun Peng
This paper is devoted to the study of the asset allocation problem for a DC pension plan with minimum guarantee constraint in a hidden Markov regime-switching economy. Suppose that four types of assets are available in the financial market: a risk-free asset, a zero-coupon bond, an inflation-indexed bond and a stock. The expected return rate of the stock depends on unobservable economic states, and the change of states is described by a hidden Markov chain. In addition, the CIR process is used to describe the evolution of the nominal interest rate. The contribution rate is also assumed to be stochastic. The goal of investment management is to minimize the convex risk measure of the terminal wealth in excess of the minimum guarantee constraint. First, we transform the partially observable optimization problem into the one with complete information using the Wonham filtering technique and deal with the minimum guarantee constraint by constructing auxiliary processes. Furthermore, we derive the optimal investment strategy by the BSDE approach. Finally, some numerical results are presented to illustrate the impacts of some important parameters on investment behaviors.
{"title":"Asset allocation for a DC pension plan with minimum guarantee constraint and hidden Markov regime-switching","authors":"Liuling Luo, Xingchun Peng","doi":"10.1017/s0269964822000419","DOIUrl":"https://doi.org/10.1017/s0269964822000419","url":null,"abstract":"This paper is devoted to the study of the asset allocation problem for a DC pension plan with minimum guarantee constraint in a hidden Markov regime-switching economy. Suppose that four types of assets are available in the financial market: a risk-free asset, a zero-coupon bond, an inflation-indexed bond and a stock. The expected return rate of the stock depends on unobservable economic states, and the change of states is described by a hidden Markov chain. In addition, the CIR process is used to describe the evolution of the nominal interest rate. The contribution rate is also assumed to be stochastic. The goal of investment management is to minimize the convex risk measure of the terminal wealth in excess of the minimum guarantee constraint. First, we transform the partially observable optimization problem into the one with complete information using the Wonham filtering technique and deal with the minimum guarantee constraint by constructing auxiliary processes. Furthermore, we derive the optimal investment strategy by the BSDE approach. Finally, some numerical results are presented to illustrate the impacts of some important parameters on investment behaviors.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73641688","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}
Pub Date : 2022-11-11DOI: 10.1017/s0269964822000377
Mahdi Alimohammadi
<p>Let <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline2.png"/><span data-mathjax-type="texmath"><span>$V_{(r,n,tilde {m}_n,k)}^{(p)}$</span></span></span></span> and <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline3.png"/><span data-mathjax-type="texmath"><span>$W_{(r,n,tilde {m}_n,k)}^{(p)}$</span></span></span></span> be the <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline4.png"/><span data-mathjax-type="texmath"><span>$p$</span></span></span></span>-spacings of generalized order statistics based on absolutely continuous distribution functions <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline5.png"/><span data-mathjax-type="texmath"><span>$F$</span></span></span></span> and <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline6.png"/><span data-mathjax-type="texmath"><span>$G$</span></span></span></span>, respectively. Imposing some conditions on <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline7.png"/><span data-mathjax-type="texmath"><span>$F$</span></span></span></span> and <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline8.png"/><span data-mathjax-type="texmath"><span>$G$</span></span></span></span> and assuming that <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline9.png"/><span data-mathjax-type="texmath"><span>$m_1=cdots =m_{n-1}$</span></span></span></span>, Hu and Zhuang (2006. Stochastic orderings between <span>p</span>-spacings of generalized order statistics from two samples. <span>Probability in the Engineering and Informational Sciences</span> 20: 475) established <span><span><img data-mimesubtype="png" data-type="" src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline10.png"/><span data-mathjax-type="texmath"><span>$V_{(r,n,tilde {m}_n,k)}^{(p)} leq _{{rm hr}} W_{(r,n,til
设$V_{(r,n,tilde {m}_n,k)}^{(p)}$和$W_{(r,n,tilde {m}_n,k)}^{(p)}$分别为基于绝对连续分布函数$F$和$G$的广义序统计量的$p$ -间距。对$F$和$G$施加一定条件，并假设$m_1=cdots =m_{n-1}$, Hu and Zhuang(2006)。两样本广义序统计量p-间隔间的随机排序。工程与信息科学中的概率(20:475)为$p=1$建立了$V_{(r,n,tilde {m}_n,k)}^{(p)} leq _{{rm hr}} W_{(r,n,tilde {m}_n,k)}^{(p)}$，并将$pgeq 2$作为一个开放的问题。在本文中，我们不仅解决了这个问题，而且给出了不相等$m_i$的结果。值得一提的是，到目前为止，即使对于普通阶统计量，这个问题也没有得到证明。
{"title":"Resolving an open problem on the hazard rate ordering of p-spacings","authors":"Mahdi Alimohammadi","doi":"10.1017/s0269964822000377","DOIUrl":"https://doi.org/10.1017/s0269964822000377","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline2.png\"/><span data-mathjax-type=\"texmath\"><span>$V_{(r,n,tilde {m}_n,k)}^{(p)}$</span></span></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline3.png\"/><span data-mathjax-type=\"texmath\"><span>$W_{(r,n,tilde {m}_n,k)}^{(p)}$</span></span></span></span> be the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline4.png\"/><span data-mathjax-type=\"texmath\"><span>$p$</span></span></span></span>-spacings of generalized order statistics based on absolutely continuous distribution functions <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline5.png\"/><span data-mathjax-type=\"texmath\"><span>$F$</span></span></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline6.png\"/><span data-mathjax-type=\"texmath\"><span>$G$</span></span></span></span>, respectively. Imposing some conditions on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline7.png\"/><span data-mathjax-type=\"texmath\"><span>$F$</span></span></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline8.png\"/><span data-mathjax-type=\"texmath\"><span>$G$</span></span></span></span> and assuming that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline9.png\"/><span data-mathjax-type=\"texmath\"><span>$m_1=cdots =m_{n-1}$</span></span></span></span>, Hu and Zhuang (2006. Stochastic orderings between <span>p</span>-spacings of generalized order statistics from two samples. <span>Probability in the Engineering and Informational Sciences</span> 20: 475) established <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230911112630604-0950:S0269964822000377:S0269964822000377_inline10.png\"/><span data-mathjax-type=\"texmath\"><span>$V_{(r,n,tilde {m}_n,k)}^{(p)} leq _{{rm hr}} W_{(r,n,til","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"15 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539063","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}
Pub Date : 2022-11-10DOI: 10.1017/s0269964822000365
Miaomiao Yu, Yinghui Tang
As the queue becomes exhausted, different maintenance tasks can be performed according to the fatigue load and wear degree of the service equipment. At the same time, considering the customer's sensitivity to time delay, the service facility will not completely remain inactive during the maintenance period. To describe this objectively existing phenomenon arising in the waiting line system, we consider a hyper-exponential working vacation queue with a batch renewal arrival process. Through the calculation of the well-structured roots of the associated characteristic equation, the shift operator method in the theory of difference equations and the supplementary variable technique for stochastic modeling plays a central role in the queue-length distribution analysis. Comparison with other ways to analyze queueing models, the advantage of our approach is that we can avoid deriving the complex transition probability matrix of the queue-length process embedded at input points. The feasibility of this approach is verified by extensive numerical examples.
{"title":"Analyzing a single hyper-exponential working vacation queue from its governing difference equation","authors":"Miaomiao Yu, Yinghui Tang","doi":"10.1017/s0269964822000365","DOIUrl":"https://doi.org/10.1017/s0269964822000365","url":null,"abstract":"\u0000 As the queue becomes exhausted, different maintenance tasks can be performed according to the fatigue load and wear degree of the service equipment. At the same time, considering the customer's sensitivity to time delay, the service facility will not completely remain inactive during the maintenance period. To describe this objectively existing phenomenon arising in the waiting line system, we consider a hyper-exponential working vacation queue with a batch renewal arrival process. Through the calculation of the well-structured roots of the associated characteristic equation, the shift operator method in the theory of difference equations and the supplementary variable technique for stochastic modeling plays a central role in the queue-length distribution analysis. Comparison with other ways to analyze queueing models, the advantage of our approach is that we can avoid deriving the complex transition probability matrix of the queue-length process embedded at input points. The feasibility of this approach is verified by extensive numerical examples.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"4 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76317586","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}
Pub Date : 2022-11-02DOI: 10.1017/S0269964822000353
Jiannan Zhang, Ping Chen, Z. Jin, Shuanming Li
This paper studies the open-loop equilibrium strategies for a class of non-zero-sum reinsurance–investment stochastic differential games between two insurers with a state-dependent mean expectation in the incomplete market. Both insurers are able to purchase proportional reinsurance contracts and invest their wealth in a risk-free asset and a risky asset whose price is modeled by a general stochastic volatility model. The surplus processes of two insurers are driven by two standard Brownian motions. The objective for each insurer is to find the equilibrium investment and reinsurance strategies to balance the expected return and variance of relative terminal wealth. Incorporating the forward backward stochastic differential equations (FBSDEs), we derive the sufficient conditions and obtain the general solutions of equilibrium controls for two insurers. Furthermore, we apply our theoretical results to two special stochastic volatility models (Hull–White model and Heston model). Numerical examples are also provided to illustrate our results.
{"title":"A class of non-zero-sum stochastic differential games between two mean–variance insurers under stochastic volatility","authors":"Jiannan Zhang, Ping Chen, Z. Jin, Shuanming Li","doi":"10.1017/S0269964822000353","DOIUrl":"https://doi.org/10.1017/S0269964822000353","url":null,"abstract":"This paper studies the open-loop equilibrium strategies for a class of non-zero-sum reinsurance–investment stochastic differential games between two insurers with a state-dependent mean expectation in the incomplete market. Both insurers are able to purchase proportional reinsurance contracts and invest their wealth in a risk-free asset and a risky asset whose price is modeled by a general stochastic volatility model. The surplus processes of two insurers are driven by two standard Brownian motions. The objective for each insurer is to find the equilibrium investment and reinsurance strategies to balance the expected return and variance of relative terminal wealth. Incorporating the forward backward stochastic differential equations (FBSDEs), we derive the sufficient conditions and obtain the general solutions of equilibrium controls for two insurers. Furthermore, we apply our theoretical results to two special stochastic volatility models (Hull–White model and Heston model). Numerical examples are also provided to illustrate our results.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":"491 - 517"},"PeriodicalIF":1.1,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82071592","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}
Pub Date : 2022-10-31DOI: 10.1017/S0269964822000341
Jingchao Li, Zichen Fang, Ciyu Nie, Sizhe Chen
Abstract Network mutual aid platforms is one of the popular risk-sharing models in recent years, and they have almost 200 million members in China. However, current mutual aid platforms does not satisfy the actuarial rules in either the apportionment method or the pricing principle. Hence, a variety of mutual aid models which enable mutual aid members with different risks to exchange their risks in a transparent and actuarial fair way have been proposed in this paper. Besides, the decision-making frameworks for participants choosing between the mutual aid platform and similar insurance products, or choosing no risk sharing are constructed, respectively. Decisions are made based on the principle of maximizing expected utility. Moreover, the optimization problems of maximizing profit and minimizing risk are constructed, respectively. Through the principle of individual fairness and relative fairness, the problem of adverse selection of the platform can also be reduced. Finally, the actual mutual aid plan is compared with similar insurance products to discuss the advantages of the optimized plan.
{"title":"Optimal design for network mutual aid","authors":"Jingchao Li, Zichen Fang, Ciyu Nie, Sizhe Chen","doi":"10.1017/S0269964822000341","DOIUrl":"https://doi.org/10.1017/S0269964822000341","url":null,"abstract":"Abstract Network mutual aid platforms is one of the popular risk-sharing models in recent years, and they have almost 200 million members in China. However, current mutual aid platforms does not satisfy the actuarial rules in either the apportionment method or the pricing principle. Hence, a variety of mutual aid models which enable mutual aid members with different risks to exchange their risks in a transparent and actuarial fair way have been proposed in this paper. Besides, the decision-making frameworks for participants choosing between the mutual aid platform and similar insurance products, or choosing no risk sharing are constructed, respectively. Decisions are made based on the principle of maximizing expected utility. Moreover, the optimization problems of maximizing profit and minimizing risk are constructed, respectively. Through the principle of individual fairness and relative fairness, the problem of adverse selection of the platform can also be reduced. Finally, the actual mutual aid plan is compared with similar insurance products to discuss the advantages of the optimized plan.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"212 1","pages":"567 - 596"},"PeriodicalIF":1.1,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85525884","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}
Pub Date : 2022-10-28DOI: 10.1017/s026996482200033x
Letian Yu, Fraser Daly, Oliver Johnson
We consider the problem of group testing (pooled testing), first introduced by Dorfman. For nonadaptive testing strategies, we refer to a nondefective item as “intruding” if it only appears in positive tests. Such items cause misclassification errors in the well-known COMP algorithm and can make other algorithms produce an error. It is therefore of interest to understand the distribution of the number of intruding items. We show that, under Bernoulli matrix designs, this distribution is well approximated in a variety of senses by a negative binomial distribution, allowing us to understand the performance of the two-stage conservative group testing algorithm of Aldridge.
{"title":"A negative binomial approximation in group testing","authors":"Letian Yu, Fraser Daly, Oliver Johnson","doi":"10.1017/s026996482200033x","DOIUrl":"https://doi.org/10.1017/s026996482200033x","url":null,"abstract":"<p>We consider the problem of group testing (pooled testing), first introduced by Dorfman. For nonadaptive testing strategies, we refer to a nondefective item as “intruding” if it only appears in positive tests. Such items cause misclassification errors in the well-known COMP algorithm and can make other algorithms produce an error. It is therefore of interest to understand the distribution of the number of intruding items. We show that, under Bernoulli matrix designs, this distribution is well approximated in a variety of senses by a negative binomial distribution, allowing us to understand the performance of the two-stage conservative group testing algorithm of Aldridge.</p>","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"10 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539065","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}
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 $mgeq 1$ possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of $m$ 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.
在通常的冲击模型中，冲击来自单一来源。Bozbulut and Eryilmaz[2020]。广义极端冲击模型及其应用。统计通讯-模拟与计算[49(1):110-120]在冲击来自$mgeq 1$可能来源之一时介绍了两种类型的极端冲击模型。在模型1中，随着时间的推移，冲击来自不同的来源。在模型2中，最初，冲击随机地来自$m$源之一，并且冲击继续从同一源到达。本文证明了在通常的随机排序下，模型1的寿命小于模型2。我们进一步证明，如果冲击到达间隔时间具有递增的故障率分布，则通常的随机排序可以推广到危害率排序。我们使用多数化的概念研究了模型2的寿命相对于冲击严重程度的随机行为。我们应用新的随机排序结果表明，模型1下的年龄替代政策比模型2下的成本更高。
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Pub Date : 2022-10-01DOI: 10.1017/s0269964822000390
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