Pub Date : 2021-10-08DOI: 10.1017/S0269964821000450
H. Mahmoud
Abstract By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.
{"title":"Covariances in Pólya urn schemes","authors":"H. Mahmoud","doi":"10.1017/S0269964821000450","DOIUrl":"https://doi.org/10.1017/S0269964821000450","url":null,"abstract":"Abstract By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"89 1","pages":"60 - 71"},"PeriodicalIF":1.1,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88694567","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 : 2021-10-01DOI: 10.1017/s0269964820000455
{"title":"ALGEBRAIC RELIABILITY OF MULTI-STATE k-OUT-OF-n SYSTEMS—CORRIGENDUM","authors":"","doi":"10.1017/s0269964820000455","DOIUrl":"https://doi.org/10.1017/s0269964820000455","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"423 1","pages":"1005 - 1005"},"PeriodicalIF":1.1,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78170950","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 : 2021-10-01DOI: 10.1017/s0269964821000474
{"title":"PES volume 35 issue 4 Cover and Front matter","authors":"","doi":"10.1017/s0269964821000474","DOIUrl":"https://doi.org/10.1017/s0269964821000474","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"1 1","pages":"f1 - f2"},"PeriodicalIF":1.1,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89170912","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 : 2021-10-01DOI: 10.1017/s0269964821000462
{"title":"PES volume 35 issue 4 Cover and Back matter","authors":"","doi":"10.1017/s0269964821000462","DOIUrl":"https://doi.org/10.1017/s0269964821000462","url":null,"abstract":"","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"4 1","pages":"b1 - b2"},"PeriodicalIF":1.1,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85242213","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 : 2021-09-28DOI: 10.1017/S0269964821000449
Idir Arab, M. Hadjikyriakou, P. E. Oliveira, Beatriz Santos
Abstract The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.
{"title":"Star-shaped order for distributions characterized by several parameters and some applications","authors":"Idir Arab, M. Hadjikyriakou, P. E. Oliveira, Beatriz Santos","doi":"10.1017/S0269964821000449","DOIUrl":"https://doi.org/10.1017/S0269964821000449","url":null,"abstract":"Abstract The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions. Journal of Applied Probability 15(2): 426–432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"8 1","pages":"49 - 59"},"PeriodicalIF":1.1,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85108956","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 : 2021-09-24DOI: 10.1017/S0269964821000437
Bin Lu, Jiandong Zhang, Rongfang Yan
Abstract This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.
{"title":"Optimal allocation of a coherent system with statistical dependent subsystems","authors":"Bin Lu, Jiandong Zhang, Rongfang Yan","doi":"10.1017/S0269964821000437","DOIUrl":"https://doi.org/10.1017/S0269964821000437","url":null,"abstract":"Abstract This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"17 1","pages":"29 - 48"},"PeriodicalIF":1.1,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89375837","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 : 2021-09-17DOI: 10.1017/S0269964821000425
T. Sahoo, Nil Kamal Hazra
Abstract Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas. We study some stochastic comparisons results for series, parallel, and general $r$-out-of-$n$ systems. Furthermore, we investigate whether a system of used components performs better than a used system with respect to different stochastic orders. Furthermore, some aging properties of these systems have been studied. Finally, some numerical examples are given to illustrate the proposed results.
{"title":"Ordering and aging properties of systems with dependent components governed by the Archimedean copula","authors":"T. Sahoo, Nil Kamal Hazra","doi":"10.1017/S0269964821000425","DOIUrl":"https://doi.org/10.1017/S0269964821000425","url":null,"abstract":"Abstract Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas. We study some stochastic comparisons results for series, parallel, and general $r$-out-of-$n$ systems. Furthermore, we investigate whether a system of used components performs better than a used system with respect to different stochastic orders. Furthermore, some aging properties of these systems have been studied. Finally, some numerical examples are given to illustrate the proposed results.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"61 1","pages":"1 - 28"},"PeriodicalIF":1.1,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81292810","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 : 2021-09-10DOI: 10.1017/S0269964821000401
Rongfang Yan, Junrui Wang, Bin Lu
This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.
{"title":"Orderings of component level versus system level at active redundancies for coherent systems with dependent components","authors":"Rongfang Yan, Junrui Wang, Bin Lu","doi":"10.1017/S0269964821000401","DOIUrl":"https://doi.org/10.1017/S0269964821000401","url":null,"abstract":"This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"117 1","pages":"1275 - 1297"},"PeriodicalIF":1.1,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73711767","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 : 2021-09-01DOI: 10.1017/S0269964821000395
Yannik Peeters, Arnoud V. den Boer
Abstract In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $sqrt {NT}$, where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $sqrt {N T}$. Our result implies that policies that achieve ${{mathcal {O}}}(sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.
{"title":"A regret lower bound for assortment optimization under the capacitated MNL model with arbitrary revenue parameters","authors":"Yannik Peeters, Arnoud V. den Boer","doi":"10.1017/S0269964821000395","DOIUrl":"https://doi.org/10.1017/S0269964821000395","url":null,"abstract":"Abstract In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $sqrt {NT}$, where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $sqrt {N T}$. Our result implies that policies that achieve ${{mathcal {O}}}(sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"30 1","pages":"1266 - 1274"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75339041","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 : 2021-08-26DOI: 10.1017/S0269964821000309
A. Mészáros, M. Telek
Abstract Concentrated random variables are frequently used in representing deterministic delays in stochastic models. The squared coefficient of variation ($mathrm {SCV}$) of the most concentrated phase-type distribution of order $N$ is $1/N$. To further reduce the $mathrm {SCV}$, concentrated matrix exponential (CME) distributions with complex eigenvalues were investigated recently. It was obtained that the $mathrm {SCV}$ of an order $N$ CME distribution can be less than $n^{-2.1}$ for odd $N=2n+1$ orders, and the matrix exponential distribution, which exhibits such a low $mathrm {SCV}$ has complex eigenvalues. In this paper, we consider CME distributions with real eigenvalues (CME-R). We present efficient numerical methods for identifying a CME-R distribution with smallest SCV for a given order $n$. Our investigations show that the $mathrm {SCV}$ of the most concentrated CME-R of order $N=2n+1$ is less than $n^{-1.85}$. We also discuss how CME-R can be used for numerical inverse Laplace transformation, which is beneficial when the Laplace transform function is impossible to evaluate at complex points.
{"title":"Concentrated matrix exponential distributions with real eigenvalues","authors":"A. Mészáros, M. Telek","doi":"10.1017/S0269964821000309","DOIUrl":"https://doi.org/10.1017/S0269964821000309","url":null,"abstract":"Abstract Concentrated random variables are frequently used in representing deterministic delays in stochastic models. The squared coefficient of variation ($mathrm {SCV}$) of the most concentrated phase-type distribution of order $N$ is $1/N$. To further reduce the $mathrm {SCV}$, concentrated matrix exponential (CME) distributions with complex eigenvalues were investigated recently. It was obtained that the $mathrm {SCV}$ of an order $N$ CME distribution can be less than $n^{-2.1}$ for odd $N=2n+1$ orders, and the matrix exponential distribution, which exhibits such a low $mathrm {SCV}$ has complex eigenvalues. In this paper, we consider CME distributions with real eigenvalues (CME-R). We present efficient numerical methods for identifying a CME-R distribution with smallest SCV for a given order $n$. Our investigations show that the $mathrm {SCV}$ of the most concentrated CME-R of order $N=2n+1$ is less than $n^{-1.85}$. We also discuss how CME-R can be used for numerical inverse Laplace transformation, which is beneficial when the Laplace transform function is impossible to evaluate at complex points.","PeriodicalId":54582,"journal":{"name":"Probability in the Engineering and Informational Sciences","volume":"61 1","pages":"1171 - 1187"},"PeriodicalIF":1.1,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80231979","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}
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