This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market in...This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.展开更多
In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ...In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.展开更多
Recently,the Darna distribution has been introduced as a new lifetime distribution.The two-parameter Darna distribution represents is a mixture of two well-known gamma and exponential distributions.A manufacturer or a...Recently,the Darna distribution has been introduced as a new lifetime distribution.The two-parameter Darna distribution represents is a mixture of two well-known gamma and exponential distributions.A manufacturer or an engineer of products conducts life testing to examine whether the quality level of products meets the customer’s requirements,such as reliability or the minimum lifetime.In this article,an attribute modified chain sampling inspection plan based on the time truncated life test is proposed for items whose lifetime follows the Darna distribution.The plan parameters,including the sample size,the acceptance number,and the past lot result of the proposed sampling plan,are determined with the help of the two-point approach considering the acceptable quality level(AQL)and the limiting quality level(LQL).The plan parameters and the corresponding operating characteristic functions of a new plan are provided in tabular form for various Darna distribution parameters.Also,a few illustrated examples are presented for various distribution parameters.The usefulness of the proposed attribute modified chain sampling plan is investigated using two real failure time datasets.The results indicate that the proposed sampling plan can reduce the sample size when the termination ratio increases for fixed values of the producer’s risk and acceptance number.Hence,the proposed attribute modified chain sampling inspection plan is recommended to practitioners in the field.展开更多
Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur t...Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur that the Bayesian approach is the best approach to make a correct decision,when historical knowledge is available.This paper suggests a Bayesian new group chain sampling plan(BNGChSP)to estimate average probability of acceptance.Binomial distribution function is used to differentiate between defective and non-defective products.Beta distribution is considered as a suitable prior distribution.Derivation is completed for the estimation of the average proportion of defectives.This study includes four quality regions namely:(i)probabilistic quality region(PQR),(ii)quality decision region(QDR),(iii)limiting quality region(LQR),and(iv)indifference quality region(IQR).The estimated values for the BNGChSPare tabulated and the inflection point values are derived,based on different combinations of design parameters including both consumer’s and producer’s risks.For comparison with the existing plan,the operating characteristic curves expose that BNGChSP is a better substitute for industrial practitioners.展开更多
Acceptance sampling is used to decide either the whole lot will be accepted or rejected,based on inspection of randomly sampled items from the same lot.As an alternative to traditional sampling plans,it is possible to...Acceptance sampling is used to decide either the whole lot will be accepted or rejected,based on inspection of randomly sampled items from the same lot.As an alternative to traditional sampling plans,it is possible to use Baye-sian approaches using previous knowledge on process variation.This study pre-sents a Bayesian two-sided group chain sampling plan(BTSGChSP)by using various combinations of design parameters.In BTSGChSP,inspection is based on preceding as well as succeeding lots.Poisson function is used to derive the probability of lot acceptance based on defective and non-defective products.Gamma distribution is considered as a suitable prior for Poisson distribution.Four quality regions are found,namely:(i)quality decision region(QDR),(ii)probabil-istic quality region(PQR),(iii)limiting quality region(LQR)and(iv)indifference quality region(IQR).Producer’s risk and consumer’s risk are considered to esti-mate the quality regions,where acceptable quality level(AQL)is associated with producer’s risk and limiting quality level(LQL)is associated with consumer’s risk.Moreover,AQL and LQL are used in the selection of design parameters for BTSGChSP.The values based on all possible combinations of design parameters for BTSGChSP are presented and inflection points’values are found.Thefinding exposes that BTSGChSP is a better substitute for the existing plan for industrial practitioners.展开更多
This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectatio...This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.展开更多
文摘This paper analyzes the relationship between the risk factor of each stock and the portfolio’s risk based on a small portfolio with four U.S.stocks,and the reason why these risk factors can be regarded as a market invariant.Then,it evaluates the properties of the convex and coherent risk indicators of the capital requirement index composed of VaR and ES,and use three methods(the historical estimation method,boudoukh’s mixed method and Monte Carlo method)to estimate the risk measurement indicators VaR and ES respectively based on the assumption of multivariate normal distribution’risk factors and multivariate student t-copula distribution’s one,finally it figures out that these three calculation results are very close.
基金funding this work through the Research Groups Program under Grant Number R.G.P.2/68/41.I.A.
文摘In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.
基金A.R.A.Alanzi would like to thank the Deanship of Scientific Research at Majmaah University for financial support and encouragement.
文摘Recently,the Darna distribution has been introduced as a new lifetime distribution.The two-parameter Darna distribution represents is a mixture of two well-known gamma and exponential distributions.A manufacturer or an engineer of products conducts life testing to examine whether the quality level of products meets the customer’s requirements,such as reliability or the minimum lifetime.In this article,an attribute modified chain sampling inspection plan based on the time truncated life test is proposed for items whose lifetime follows the Darna distribution.The plan parameters,including the sample size,the acceptance number,and the past lot result of the proposed sampling plan,are determined with the help of the two-point approach considering the acceptable quality level(AQL)and the limiting quality level(LQL).The plan parameters and the corresponding operating characteristic functions of a new plan are provided in tabular form for various Darna distribution parameters.Also,a few illustrated examples are presented for various distribution parameters.The usefulness of the proposed attribute modified chain sampling plan is investigated using two real failure time datasets.The results indicate that the proposed sampling plan can reduce the sample size when the termination ratio increases for fixed values of the producer’s risk and acceptance number.Hence,the proposed attribute modified chain sampling inspection plan is recommended to practitioners in the field.
基金This research was supported by the Ministry of Education(MOE)through Fundamental Research Grant Scheme(FRGS/1/2020/STG06/UUM/02/2),S/O Code 14884.
文摘Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur that the Bayesian approach is the best approach to make a correct decision,when historical knowledge is available.This paper suggests a Bayesian new group chain sampling plan(BNGChSP)to estimate average probability of acceptance.Binomial distribution function is used to differentiate between defective and non-defective products.Beta distribution is considered as a suitable prior distribution.Derivation is completed for the estimation of the average proportion of defectives.This study includes four quality regions namely:(i)probabilistic quality region(PQR),(ii)quality decision region(QDR),(iii)limiting quality region(LQR),and(iv)indifference quality region(IQR).The estimated values for the BNGChSPare tabulated and the inflection point values are derived,based on different combinations of design parameters including both consumer’s and producer’s risks.For comparison with the existing plan,the operating characteristic curves expose that BNGChSP is a better substitute for industrial practitioners.
基金supported by the Ministry of Higher Education(MoHE)through Fundamental Research Grant Scheme(FRGS/1/2020/STG06/UUM/02/2).
文摘Acceptance sampling is used to decide either the whole lot will be accepted or rejected,based on inspection of randomly sampled items from the same lot.As an alternative to traditional sampling plans,it is possible to use Baye-sian approaches using previous knowledge on process variation.This study pre-sents a Bayesian two-sided group chain sampling plan(BTSGChSP)by using various combinations of design parameters.In BTSGChSP,inspection is based on preceding as well as succeeding lots.Poisson function is used to derive the probability of lot acceptance based on defective and non-defective products.Gamma distribution is considered as a suitable prior for Poisson distribution.Four quality regions are found,namely:(i)quality decision region(QDR),(ii)probabil-istic quality region(PQR),(iii)limiting quality region(LQR)and(iv)indifference quality region(IQR).Producer’s risk and consumer’s risk are considered to esti-mate the quality regions,where acceptable quality level(AQL)is associated with producer’s risk and limiting quality level(LQL)is associated with consumer’s risk.Moreover,AQL and LQL are used in the selection of design parameters for BTSGChSP.The values based on all possible combinations of design parameters for BTSGChSP are presented and inflection points’values are found.Thefinding exposes that BTSGChSP is a better substitute for the existing plan for industrial practitioners.
基金Project supported by the National Natural Science Foundation of China(No.10131040).
文摘This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
