In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariat...In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.展开更多
We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations.Our approach relies on comparison results for forward-backward...We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations.Our approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity,monotonicity,and continuous dependence properties for the solutions of associated semilinear parabolic partial differential equations.Applications to contingent claim price comparison under different hedging portfolio constraints are provided.展开更多
Accurately modeling heavy-tailed data is critical across applied sciences,particularly in finance,medicine,and actuarial analysis.This work presents the heavy-tailed power XLindley distribution(HTPXLD),a unique heavy-...Accurately modeling heavy-tailed data is critical across applied sciences,particularly in finance,medicine,and actuarial analysis.This work presents the heavy-tailed power XLindley distribution(HTPXLD),a unique heavy-tailed distribution.Adding one more parameter to the power XLindley distribution improves this new distribution,especially when modeling leptokurtic lifetime data.The suggested density provides greater flexibility with asymmetric forms and different degrees of peakedness.Its statistical features,like the quantile function,moments,extropy measures,incomplete moments,stochastic ordering,and stress-strength parameters,are explored.We further investigate its use in actuarial science through the computation of pertinent metrics,such as value-at-risk,tail value-at-risk,tail variance,and tail variance premium.To obtain the point and interval parameter estimates,we use the maximum likelihood estimation approach.We do many simulation tests to evaluate the performance of our proposed estimator.Metrics like bias,relative bias,mean squared error,root mean squared error,average interval length,and coverage probability will be used in these tests to assess the estimator’s performance.To illustrate the practical value of our proposed model,we apply it to analyze three real-world datasets.We then compare its performance to established competing models,highlighting its advantages.展开更多
This paper presents several useful mixture representations for the reliability function of the residual live of a coherent system with independent but non-identically distributed components. These presentations are ba...This paper presents several useful mixture representations for the reliability function of the residual live of a coherent system with independent but non-identically distributed components. These presentations are based on order statistics, signatures and mean reliability functions. We then discuss some stochastic comparisons of residual lives between two systems based on the stochastic ordering of coefficient vectors （or components） of the two systems. These results form nice extensions of some known results for the case of independent and identically distributed components.展开更多
In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to st...In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.展开更多
Coherent systems are very important in reliability,survival analysis and other life sciences.In this paper,we consider the number of failed components in an(n-k+1)-out-of-n system,given that at least m(m<k≤n)compo...Coherent systems are very important in reliability,survival analysis and other life sciences.In this paper,we consider the number of failed components in an(n-k+1)-out-of-n system,given that at least m(m<k≤n)components have failed before time t,and the system is still working at time t.In this case,we compute the probability that there are exactly i working components.First the reliability and several stochastic properties are obtained.Furthermore,we extend the results to general coherent systems with absolutely continuous and exchangeable components.展开更多
In this paper we consider a coherent system consisting of n components with independent and identically distributed components. We obtain a mixture representation of the reliability function of the residual lifetime o...In this paper we consider a coherent system consisting of n components with independent and identically distributed components. We obtain a mixture representation of the reliability function of the residual lifetime of living components of a coherent system when the system has failed. Based on the concept of s^gnature, stochastic comparisons on the residual life of two systems with stochastically ordered signatures are conducted.展开更多
In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The loga...In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.展开更多
Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL ...Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL class of life distributions if its residual life(defined as a conditional random vector)is decreasing in time under convex or linear order.Some conservation properties of these classes are studied.展开更多
In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-...In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-down bathtub and J-shaped hazard rates making it more flexible than the Hamza distribution for modelling various kinds of lifetime data. A comprehensive account of the properties of this distribution is presented. The maximum likelihood estimators of the unknown model parameters are discussed. Finally, a real-life data is analyzed for illustrative purpose proving that the PH outperforms the Hamza distribution and several other lifetime distributions.展开更多
I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replac...I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replacement at each discrete-time point. The true state of the system is not known when it is operated. Instead, the system is monitored after operation and some incomplete information concerned with the deterioration is obtained for decision making. Since there are multiple imperfect repairs, I can select one option from them when the imperfect repair is preferable to operation and replacement. To express this situation, I propose a POMDP model and theoretically investigate the structure of an optimal maintenance policy minimizing a total expected discounted cost for an unbounded horizon. Then two stochastic orders are used for the analysis of our problem.展开更多
This paper considers a single-item, periodic-review inventory model with linear ordercosts, a convex function representing expected one-period costs, nonegative i.i.d. demandsand a fixed cost for order. Stockouts are ...This paper considers a single-item, periodic-review inventory model with linear ordercosts, a convex function representing expected one-period costs, nonegative i.i.d. demandsand a fixed cost for order. Stockouts are backordered. All data are stationary Both finiteand infinite horizon problems are treated.展开更多
Many dynamical systems are modeled as second order differential systems.In this paper we address the problem of controllability for second order semilinear stochastic systems in finite dimensional spaces.Sufficient cr...Many dynamical systems are modeled as second order differential systems.In this paper we address the problem of controllability for second order semilinear stochastic systems in finite dimensional spaces.Sufficient criteria for the complete controllability are formulated under some appropriate assumptions.The results are obtained by using the Banach fixed point theorem.Finally an illustrative example is provided.展开更多
In this paper,the existence of stationary oscillations of second order periodic systemsunder stochastlc noise interference is investigated,and the necessary and sufficient condition for the existence of stationary osc...In this paper,the existence of stationary oscillations of second order periodic systemsunder stochastlc noise interference is investigated,and the necessary and sufficient condition for the existence of stationary oscillations in the sense of mean-square stability is obtained via establishing equivalent vector stochastic systems and establishing deterministicequivalent systems in the sense of stability, and applying the existence theorem of stationary oscillations for the deterministic systems.展开更多
This paper studies a maintenance model for an one-unit degenerative system with multiple failure states based on the proportional hazards and proportional reversed hazards models. The authors investigate how the varia...This paper studies a maintenance model for an one-unit degenerative system with multiple failure states based on the proportional hazards and proportional reversed hazards models. The authors investigate how the variation of system configuration parameters have an impact on both operating and repair times and hence the system performance. Furthermore, the authors also derive the explicit expression for the long-run average cost per unit time. An algorithm to locate the optimal number of repairs in a renewal cycle is discussed as well.展开更多
This paper considers scheduling n jobs on a single machine where the job processing times anddue dates are independent random variables with arbitrary distribution functions.We consider the casethat the weighted job t...This paper considers scheduling n jobs on a single machine where the job processing times anddue dates are independent random variables with arbitrary distribution functions.We consider the casethat the weighted job tardiness in expectation is minimized.It is assumed that job's due dates arecompatible with processing times and weights.We show that the jobs should be sequenced indecreasing stochastic order of their due dates.展开更多
In this article,we carry out stochastic comparisons on the maximum order statistics arising from two batches of multiple-outlier gamma random variables with different shape and scale parameters.It is proved that,under...In this article,we carry out stochastic comparisons on the maximum order statistics arising from two batches of multiple-outlier gamma random variables with different shape and scale parameters.It is proved that,under certain conditions,the majorization order between the vectors of shape parameters together with the weak majorization order[p-larger order]between the vectors of scale parameters implies the likelihood ratio order[hazard rate order]between the largest order statistics.The results established here strengthen and generalize some known ones in the literature.展开更多
In this paper,we consider Marshall and Olkin’s family of distributions.The parent(baseline)distribution is taken to be a scaled family of distributions.Two models:(i)modified proportional hazard rate scale and(ii)mod...In this paper,we consider Marshall and Olkin’s family of distributions.The parent(baseline)distribution is taken to be a scaled family of distributions.Two models:(i)modified proportional hazard rate scale and(ii)modified proportional reversed hazard rate scale,are considered.Some stochastic comparison results in terms of the usual stochastic,hazard rate and reversed hazard rate orders are studied to compare order statistics formed from two sets of independent observations following these models.Most of the sufficient conditions are obtained depending on various majorizationtype partial orderings.Further,the setup with multiple-outlier model is taken.Various stochastic orders between the smallest and largest order statistics are developed.Several numerical examples are provided to illustrate the effectiveness of the established theoretical results.展开更多
This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n sys-tems with heterogeneous components.The expectation order,the increasing convex/concave order and the usual stochastic orde...This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n sys-tems with heterogeneous components.The expectation order,the increasing convex/concave order and the usual stochastic order are employed to investigate stochastic behaviours of sys-tem capacity.Sufficient conditions are established in terms of majorisation-type orders between the vectors of component lifetime distribution parameters and the vectors of weights.Some examples are also provided as illustrations.展开更多
This article introduces a three-parameter Lehman-type t distribution having 2 degrees of freedom,that is capable of fitting positive and negative skewed data sets.It is shown that the density and hazard functions of t...This article introduces a three-parameter Lehman-type t distribution having 2 degrees of freedom,that is capable of fitting positive and negative skewed data sets.It is shown that the density and hazard functions of the proposed distribution are uni-model.Ordinary moments,entropy measure,ordering,identifiability and order statistics are investigated.Since the quantile function is explicitly defined,quantile-based statistics are also discussed for the proposed distribution.These properties include measures of skewness and kurtosis,L-moments,quantile density and hazard functions,mean residual life function and Parzen's score function.Mechanisms of maximum likelihood,bias correction and matching of percentiles are employed for estimating the unknown parameters of the distribution.Simulation experiments are conducted to compare the performance of these three estimation methods.A real-life data set consisting of strength of glass fibres is fitted to show the adequacy of the proposed distribution over some extensions of the normal and t distributions.Parametric regression model is developed along with its parameter estimation using the maximum likelihood approach.Simulation study for the regression model is also presented that endorsed the asymptotic properties of the estimators.展开更多
文摘In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.
基金This research is supported by the Ministry of Education,Singapore(Grant No.MOE2018-T1-001-201)。
文摘We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations.Our approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity,monotonicity,and continuous dependence properties for the solutions of associated semilinear parabolic partial differential equations.Applications to contingent claim price comparison under different hedging portfolio constraints are provided.
基金supported by researchers Supporting Project Number(RSPD2025R548)King Saud University,Riyadh,Saudi Arabia.
文摘Accurately modeling heavy-tailed data is critical across applied sciences,particularly in finance,medicine,and actuarial analysis.This work presents the heavy-tailed power XLindley distribution(HTPXLD),a unique heavy-tailed distribution.Adding one more parameter to the power XLindley distribution improves this new distribution,especially when modeling leptokurtic lifetime data.The suggested density provides greater flexibility with asymmetric forms and different degrees of peakedness.Its statistical features,like the quantile function,moments,extropy measures,incomplete moments,stochastic ordering,and stress-strength parameters,are explored.We further investigate its use in actuarial science through the computation of pertinent metrics,such as value-at-risk,tail value-at-risk,tail variance,and tail variance premium.To obtain the point and interval parameter estimates,we use the maximum likelihood estimation approach.We do many simulation tests to evaluate the performance of our proposed estimator.Metrics like bias,relative bias,mean squared error,root mean squared error,average interval length,and coverage probability will be used in these tests to assess the estimator’s performance.To illustrate the practical value of our proposed model,we apply it to analyze three real-world datasets.We then compare its performance to established competing models,highlighting its advantages.
基金supported by the National Natural Science Foundation of China(1116102871361020)
文摘This paper presents several useful mixture representations for the reliability function of the residual live of a coherent system with independent but non-identically distributed components. These presentations are based on order statistics, signatures and mean reliability functions. We then discuss some stochastic comparisons of residual lives between two systems based on the stochastic ordering of coefficient vectors （or components） of the two systems. These results form nice extensions of some known results for the case of independent and identically distributed components.
文摘In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1116102871361020)
文摘Coherent systems are very important in reliability,survival analysis and other life sciences.In this paper,we consider the number of failed components in an(n-k+1)-out-of-n system,given that at least m(m<k≤n)components have failed before time t,and the system is still working at time t.In this case,we compute the probability that there are exactly i working components.First the reliability and several stochastic properties are obtained.Furthermore,we extend the results to general coherent systems with absolutely continuous and exchangeable components.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1116102871361020)
文摘In this paper we consider a coherent system consisting of n components with independent and identically distributed components. We obtain a mixture representation of the reliability function of the residual lifetime of living components of a coherent system when the system has failed. Based on the concept of s^gnature, stochastic comparisons on the residual life of two systems with stochastically ordered signatures are conducted.
基金The NSF(10971081,11001105,11071126,10926156,11071269,J0730101)of ChinaSpecialized Research Fund(20070183023)for the Doctoral Program of Higher Education+2 种基金Program(NCET-08-237)for New Century Excellent Talents in UniversityScientific Research Fund(200810024,200903278)of Jilin University985 project of Jilin University
文摘In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.
文摘Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL class of life distributions if its residual life(defined as a conditional random vector)is decreasing in time under convex or linear order.Some conservation properties of these classes are studied.
文摘In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-down bathtub and J-shaped hazard rates making it more flexible than the Hamza distribution for modelling various kinds of lifetime data. A comprehensive account of the properties of this distribution is presented. The maximum likelihood estimators of the unknown model parameters are discussed. Finally, a real-life data is analyzed for illustrative purpose proving that the PH outperforms the Hamza distribution and several other lifetime distributions.
文摘I consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state. When the system is put into practice, I may select operation (wait), imperfect repair, or replacement at each discrete-time point. The true state of the system is not known when it is operated. Instead, the system is monitored after operation and some incomplete information concerned with the deterioration is obtained for decision making. Since there are multiple imperfect repairs, I can select one option from them when the imperfect repair is preferable to operation and replacement. To express this situation, I propose a POMDP model and theoretically investigate the structure of an optimal maintenance policy minimizing a total expected discounted cost for an unbounded horizon. Then two stochastic orders are used for the analysis of our problem.
文摘This paper considers a single-item, periodic-review inventory model with linear ordercosts, a convex function representing expected one-period costs, nonegative i.i.d. demandsand a fixed cost for order. Stockouts are backordered. All data are stationary Both finiteand infinite horizon problems are treated.
基金supported by the University Grants Commission F.510/7/DRS-1/2016(SAP-I)supported by the National Research Foundation of Korea NRF-2013R1A1A2A10006693.
文摘Many dynamical systems are modeled as second order differential systems.In this paper we address the problem of controllability for second order semilinear stochastic systems in finite dimensional spaces.Sufficient criteria for the complete controllability are formulated under some appropriate assumptions.The results are obtained by using the Banach fixed point theorem.Finally an illustrative example is provided.
文摘In this paper,the existence of stationary oscillations of second order periodic systemsunder stochastlc noise interference is investigated,and the necessary and sufficient condition for the existence of stationary oscillations in the sense of mean-square stability is obtained via establishing equivalent vector stochastic systems and establishing deterministicequivalent systems in the sense of stability, and applying the existence theorem of stationary oscillations for the deterministic systems.
基金supported by the National Natural Science Foundation of China under Grant No.11422109
文摘This paper studies a maintenance model for an one-unit degenerative system with multiple failure states based on the proportional hazards and proportional reversed hazards models. The authors investigate how the variation of system configuration parameters have an impact on both operating and repair times and hence the system performance. Furthermore, the authors also derive the explicit expression for the long-run average cost per unit time. An algorithm to locate the optimal number of repairs in a renewal cycle is discussed as well.
文摘This paper considers scheduling n jobs on a single machine where the job processing times anddue dates are independent random variables with arbitrary distribution functions.We consider the casethat the weighted job tardiness in expectation is minimized.It is assumed that job's due dates arecompatible with processing times and weights.We show that the jobs should be sequenced indecreasing stochastic order of their due dates.
基金the financial support from the start-up grant at Nankai Universitythe Fundamental Research Funds for the Central Universities,Nankai University(No.63201159,No.63211091)+2 种基金the financial support from the Natural Science Foundation of Tianjin(No.20JCQNJC01740)the support from National Natural Science Foundation of China(11871252)A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘In this article,we carry out stochastic comparisons on the maximum order statistics arising from two batches of multiple-outlier gamma random variables with different shape and scale parameters.It is proved that,under certain conditions,the majorization order between the vectors of shape parameters together with the weak majorization order[p-larger order]between the vectors of scale parameters implies the likelihood ratio order[hazard rate order]between the largest order statistics.The results established here strengthen and generalize some known ones in the literature.
基金Suchandan Kayal gratefully acknowledges the partial financial support for this research work under a grant MTR/2018/000350 SERB,India.
文摘In this paper,we consider Marshall and Olkin’s family of distributions.The parent(baseline)distribution is taken to be a scaled family of distributions.Two models:(i)modified proportional hazard rate scale and(ii)modified proportional reversed hazard rate scale,are considered.Some stochastic comparison results in terms of the usual stochastic,hazard rate and reversed hazard rate orders are studied to compare order statistics formed from two sets of independent observations following these models.Most of the sufficient conditions are obtained depending on various majorizationtype partial orderings.Further,the setup with multiple-outlier model is taken.Various stochastic orders between the smallest and largest order statistics are developed.Several numerical examples are provided to illustrate the effectiveness of the established theoretical results.
基金The author thanks the insightful and helpful comments of an Associate Editor and an anonymous reviewer,which have improved the presentation of the paper.The author acknowledges the start-up grant in Nankai University and the Fundamental Research Funds for the Central Universities,Nankai University(No.63201159)the financial support fromthe Natural Science Foundation of Tianjin(No.20JCQNJC01740).
文摘This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n sys-tems with heterogeneous components.The expectation order,the increasing convex/concave order and the usual stochastic order are employed to investigate stochastic behaviours of sys-tem capacity.Sufficient conditions are established in terms of majorisation-type orders between the vectors of component lifetime distribution parameters and the vectors of weights.Some examples are also provided as illustrations.
基金the financial support from Science and Engineering Research Board,Department of Science&Technology,Government of India,under the scheme Early Career Research Award(file no.ECR/2017/002416)Dr.Sharma also acknowledges Banaras Hindu University,Varanasi,India,for providing financial support as seed grant under the Institute of Eminence Scheme(Scheme no.Dev.6031).
文摘This article introduces a three-parameter Lehman-type t distribution having 2 degrees of freedom,that is capable of fitting positive and negative skewed data sets.It is shown that the density and hazard functions of the proposed distribution are uni-model.Ordinary moments,entropy measure,ordering,identifiability and order statistics are investigated.Since the quantile function is explicitly defined,quantile-based statistics are also discussed for the proposed distribution.These properties include measures of skewness and kurtosis,L-moments,quantile density and hazard functions,mean residual life function and Parzen's score function.Mechanisms of maximum likelihood,bias correction and matching of percentiles are employed for estimating the unknown parameters of the distribution.Simulation experiments are conducted to compare the performance of these three estimation methods.A real-life data set consisting of strength of glass fibres is fitted to show the adequacy of the proposed distribution over some extensions of the normal and t distributions.Parametric regression model is developed along with its parameter estimation using the maximum likelihood approach.Simulation study for the regression model is also presented that endorsed the asymptotic properties of the estimators.
