In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estim...In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.展开更多
Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed...Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.展开更多
In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulatio...In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulations are conducted when Bayesian methods with Jeffery’s priors of the unknown parameters of Weibull distribution are used,while the goodness of fit analysis is conducted when the likelihood estimators are used and the corresponding empirical distributions are obtained.The ranked set sampling designs considered in this research are the usual ranked set sampling,extreme ranked set sampling,median ranked set sampling,and neoteric ranked set sampling designs.An intensive Monte Carlo simulation study is conducted using Lindley’s approximation algorithm to compute the different designs’-based estimators.The study showed that the dependent design“neoteric ranked set sampling design”is superior to other ranked set designs and the total relative efficiency is higher than the other designs’total relative efficiency.展开更多
This article proposes two new Ranked Set Sampling(RSS)designs for estimating the population parameters:Simple Z Ranked Set Sampling(SZRSS)and Generalized Z Ranked Set Sampling(GZRSS).These designs provide unbiased est...This article proposes two new Ranked Set Sampling(RSS)designs for estimating the population parameters:Simple Z Ranked Set Sampling(SZRSS)and Generalized Z Ranked Set Sampling(GZRSS).These designs provide unbiased estimators for the mean of symmetric distributions.It is shown that for non-uniform symmetric distributions,the estimators of the mean under the suggested designs are more efcient than those obtained by RSS,Simple Random Sampling(SRS),extreme RSS and truncation based RSS designs.Also,the proposed RSS schemes outperform other RSS schemes and provide more efcient estimates than their competitors under imperfect rankings.The suggested mean estimators under perfect and imperfect rankings are more efcient than the linear regression estimator under SRS.Our proposed RSS designs are also extended to cover the estimation of the population median.Real data is used to examine wthe usefulness and efciency of our estimators.展开更多
In this article,we offer a new adapted model with three parameters,called Zubair Lomax distribution.The new model can be very useful in analyzing and modeling real data and provides better fits than some others new mo...In this article,we offer a new adapted model with three parameters,called Zubair Lomax distribution.The new model can be very useful in analyzing and modeling real data and provides better fits than some others new models.Primary properties of the Zubair Lomax model are determined by moments,probability weighted moments,Renyi entropy,quantile function and stochastic ordering,among others.Maximum likelihood method is used to estimate the population parameters,owing to simple random sample and ranked set sampling schemes.The behavior of the maximum likelihood estimates for the model parameters is studied using Monte Carlo simulation.Criteria measures including biases,mean square errors and relative efficiencies are used to compare estimates.Regarding the simulation study,we observe that the estimates based on ranked set sampling are more efficient compared to the estimates based on simple random sample.The importance and flexibility of Zubair Lomax are validated empirically in modeling two types of lifetime data.展开更多
In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mea...In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.展开更多
In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(...In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.展开更多
In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries mor...In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.展开更多
The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(...The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.展开更多
Nonparametric(distribution-free)control charts have been introduced in recent years when quality characteristics do not follow a specific distribution.When the sample selection is prohibitively expensive,we prefer ran...Nonparametric(distribution-free)control charts have been introduced in recent years when quality characteristics do not follow a specific distribution.When the sample selection is prohibitively expensive,we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts.In this study,we proposed a nonparametric homogeneously weighted moving average based on theWilcoxon signed-rank test with ranked set sampling(NPHWMARSS)control chart for detecting shifts in the process location of a continuous and symmetric distribution.Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMARSS control chart.The proposed NPHWMARSS control chart’s performance is compared to that of parametric and nonparametric control charts.These control charts include the exponentially weighted moving average(EWMA)control chart,Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart,the nonparametric EWMA sign control chart,Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart,and the homogeneously weighted moving average control charts.The findings show that the proposed NPHWMARSS control chart performs better than its competitors,particularly for the small shifts.Finally,an example is presented to demonstrate how the proposed scheme can be implemented practically.展开更多
Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modifica...Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.展开更多
This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the charact...This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.展开更多
Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It...Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account, we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set sampling are always more efficient than those based on rounded simple random sampling.展开更多
In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked s...In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the Fisher information matrix for the location-scale family.The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS.In order to give more insight into the performance of MERSS with respect to simple random sampling,the Fisher information matrix for usual locationscale distributions are respectively computed under the two sampling.The numerical results show that MERSS provides more information than simple random sampling in parametric inference.展开更多
Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on th...Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.展开更多
The procedure of stratified double quartile ranked set sampling （SDQRSS） method is introduced to estimate the population mean. The SDQRSS is compared with the simple random sampling （SRS）, stratified ranked set sa...The procedure of stratified double quartile ranked set sampling （SDQRSS） method is introduced to estimate the population mean. The SDQRSS is compared with the simple random sampling （SRS）, stratified ranked set sampling （SRSS） and stratified simple random sampling （SSRS）. It is shown that SDQRSS estimator is an unbiased of the population mean and more efficient than SRS, SRSS and SSRS for symmetric and asymmetric distributions. In addition, by SDQRSS we can increase the efficiency of mean estimator for specific value of the sample size.展开更多
In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown u...In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.展开更多
This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and up...This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.展开更多
This paper presents some novel entropy estimators of a continuous random variable using simple random sampling(SRS),ranked set sampling(RSS),and double RSS(DRSS)schemes.The theoretical results of the proposed entropy ...This paper presents some novel entropy estimators of a continuous random variable using simple random sampling(SRS),ranked set sampling(RSS),and double RSS(DRSS)schemes.The theoretical results of the proposed entropy estimators are derived.The proposed entropy estimators are compared in terms of the bias and the root mean squared errors,theoretically and numerically,with the Vasicek O.[A test for normality based on sample entropy,J.R.Stat.Soc.B 38:54–59,1976.]entropy estimators using SRS,RSS,and DRSS schemes.It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.展开更多
文摘In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.
基金Supported by the National Natural Science Foundation of China(11901236)the Scientific Research Fund of Hunan Provincial Science and Technology Department(2019JJ50479)+3 种基金the Scientific Research Fund of Hunan Provincial Education Department(18B322)the Winning Bid Project of Hunan Province for the 4th National Economic Census([2020]1)the Young Core Teacher Foundation of Hunan Province([2020]43)the Funda-mental Research Fund of Xiangxi Autonomous Prefecture(2018SF5026)。
文摘Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS)was first proposed by McIntyre[1952.A method for unbiased selective sampling,using ranked sets.Australian Journal of Agricultural Research 3,385-390]as an effective way to estimate the pasture mean.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the best linear unbiased estimators(BLUEs)for the simple linear regression model.The BLUEs for this model under MERSS are derived.The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.
文摘In this paper,a joint analysis consisting of goodness-of-fit tests and Markov chain Monte Carlo simulations are used to assess the performance of some ranked set sampling designs.The Markov chain Monte Carlo simulations are conducted when Bayesian methods with Jeffery’s priors of the unknown parameters of Weibull distribution are used,while the goodness of fit analysis is conducted when the likelihood estimators are used and the corresponding empirical distributions are obtained.The ranked set sampling designs considered in this research are the usual ranked set sampling,extreme ranked set sampling,median ranked set sampling,and neoteric ranked set sampling designs.An intensive Monte Carlo simulation study is conducted using Lindley’s approximation algorithm to compute the different designs’-based estimators.The study showed that the dependent design“neoteric ranked set sampling design”is superior to other ranked set designs and the total relative efficiency is higher than the other designs’total relative efficiency.
基金The authors extend their appreciation to Deanship of Scientic Research at King Khalid University for funding this work through Research Groups Program under Grant No.R.G.P.2/68/41.I.M.A.and A.I.A.received the grant.
文摘This article proposes two new Ranked Set Sampling(RSS)designs for estimating the population parameters:Simple Z Ranked Set Sampling(SZRSS)and Generalized Z Ranked Set Sampling(GZRSS).These designs provide unbiased estimators for the mean of symmetric distributions.It is shown that for non-uniform symmetric distributions,the estimators of the mean under the suggested designs are more efcient than those obtained by RSS,Simple Random Sampling(SRS),extreme RSS and truncation based RSS designs.Also,the proposed RSS schemes outperform other RSS schemes and provide more efcient estimates than their competitors under imperfect rankings.The suggested mean estimators under perfect and imperfect rankings are more efcient than the linear regression estimator under SRS.Our proposed RSS designs are also extended to cover the estimation of the population median.Real data is used to examine wthe usefulness and efciency of our estimators.
基金funded by the Deanship of Scientific Research(DSR),King Abdul Aziz University,Jeddah,under grant No.DF-281-305-1441This work was funded by the Deanship of Scientific Research(DSR),King Abdul Aziz University,Jeddah,under grant No.DF-281-305-1441.
文摘In this article,we offer a new adapted model with three parameters,called Zubair Lomax distribution.The new model can be very useful in analyzing and modeling real data and provides better fits than some others new models.Primary properties of the Zubair Lomax model are determined by moments,probability weighted moments,Renyi entropy,quantile function and stochastic ordering,among others.Maximum likelihood method is used to estimate the population parameters,owing to simple random sample and ranked set sampling schemes.The behavior of the maximum likelihood estimates for the model parameters is studied using Monte Carlo simulation.Criteria measures including biases,mean square errors and relative efficiencies are used to compare estimates.Regarding the simulation study,we observe that the estimates based on ranked set sampling are more efficient compared to the estimates based on simple random sample.The importance and flexibility of Zubair Lomax are validated empirically in modeling two types of lifetime data.
文摘In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.
基金the National Natural Science Foundation of China(11901236)Scienti c Research Fund of Hunan Provincial Science and Technology Department(2019JJ50479)+1 种基金Scienti c Research Fund of Hunan Provincial Education Department(18B322)Fundamental Research Fund of Xiangxi Autonomous Prefec-ture(2018SF5026).
文摘In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.
基金Supported by National Science Foundation of China(11901236,12261036),Scientific Research Fund of Hunan Provincial Education Department(21A0328)Provincial Natural Science Foundation of Hunan(2022JJ30469)+1 种基金Young Core Teacher Foundation of Hunan Province([2020]43)Jishou University Laboratory Program(JDDL2017001,JDLF2021024).
文摘In the current paper,we considered the Fisher information matrix from the generalized Rayleigh distribution(GR)distribution in ranked set sampling(RSS).The numerical results show that the ranked set sample carries more information about λ and α than a simple random sample of equivalent size.In order to give more insight into the performance of RSS with respect to(w.r.t.)simple random sampling(SRS),a modified unbiased estimator and a modified best linear unbiased estimator(BLUE)of scale and shape λ and α from GR distribution in SRS and RSS are studied.The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.
基金supported by the This research was supported by National Science Foundation of China(Grant Nos.12261036 and 11901236)Provincial Natural Science Foundation of Hunan(Grant No.2022JJ30469)Scientific Research Fund of Hunan Provincial Education Department(Grant No.21A0328)。
文摘The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.
基金Funds are available under the Grant No.RGP.2/132/43 at King Khalid University,Kingdom of Saudi Arabia.
文摘Nonparametric(distribution-free)control charts have been introduced in recent years when quality characteristics do not follow a specific distribution.When the sample selection is prohibitively expensive,we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts.In this study,we proposed a nonparametric homogeneously weighted moving average based on theWilcoxon signed-rank test with ranked set sampling(NPHWMARSS)control chart for detecting shifts in the process location of a continuous and symmetric distribution.Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMARSS control chart.The proposed NPHWMARSS control chart’s performance is compared to that of parametric and nonparametric control charts.These control charts include the exponentially weighted moving average(EWMA)control chart,Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart,the nonparametric EWMA sign control chart,Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart,and the homogeneously weighted moving average control charts.The findings show that the proposed NPHWMARSS control chart performs better than its competitors,particularly for the small shifts.Finally,an example is presented to demonstrate how the proposed scheme can be implemented practically.
基金supported by the National Natural Science Foundation of China(No.11901236)the Scientific Research Fund of Hunan Provincial Science and Technology Department(No.2019JJ50479)+2 种基金the Scientific Research Fund of Hunan Provincial Education Department(No.18B322)the Young Core Teacher Foundation of Hunan Province(No.202043)the Fundamental Research Fund of Xiangxi Autonomous Prefecture(No.2018SF5026)。
文摘Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.
基金supported by the National Science Foundation of China under Grant Nos.11571133 and11461027the Fundamental Research Funds for the Central Universities under Grant No.20205001515
文摘This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.
基金The second author is supported by National Natural Science Foundation of China （Grant No. 10871036）
文摘Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account, we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set sampling are always more efficient than those based on rounded simple random sampling.
基金supported by the National Natural Science Foundation of China under Grant No.11901236Fund of Hunan Provincial Science and Technology Department under Grant No.2019JJ50479+1 种基金Fund of Hunan Provincial Education Department under Grant No.18B322Young Core Teacher Foundation of Hunan Province under Grant No.[2020]43。
文摘In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling called moving extremes ranked set sampling(MERSS)is considered for the Fisher information matrix for the location-scale family.The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS.In order to give more insight into the performance of MERSS with respect to simple random sampling,the Fisher information matrix for usual locationscale distributions are respectively computed under the two sampling.The numerical results show that MERSS provides more information than simple random sampling in parametric inference.
基金supported by the National Natural Science Foundation of China under Grant Nos.10571070 and 11001097
文摘Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.
文摘The procedure of stratified double quartile ranked set sampling （SDQRSS） method is introduced to estimate the population mean. The SDQRSS is compared with the simple random sampling （SRS）, stratified ranked set sampling （SRSS） and stratified simple random sampling （SSRS）. It is shown that SDQRSS estimator is an unbiased of the population mean and more efficient than SRS, SRSS and SSRS for symmetric and asymmetric distributions. In addition, by SDQRSS we can increase the efficiency of mean estimator for specific value of the sample size.
基金supported by National Science Foundation of China (Grant Nos.12261036 and 11901236)Scientific Research Fund of Hunan Provincial Education Department (Grant No.21A0328)+1 种基金Provincial Natural Science Foundation of Hunan (Grant No.2022JJ30469)Young Core Teacher Foundation of Hunan Province (Grant No.[2020]43)。
文摘In the current paper,the best linear unbiased estimators(BLUEs)of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling(MERSS).Explicit mathematical expressions of these estimators and their variances are derived.Their relative efficiencies with respect to the minimum variance unbiased estimators(MVUEs)under simple random sampling(SRS)are compared for the cases of some usual distributions.The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.
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This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.
文摘This paper presents some novel entropy estimators of a continuous random variable using simple random sampling(SRS),ranked set sampling(RSS),and double RSS(DRSS)schemes.The theoretical results of the proposed entropy estimators are derived.The proposed entropy estimators are compared in terms of the bias and the root mean squared errors,theoretically and numerically,with the Vasicek O.[A test for normality based on sample entropy,J.R.Stat.Soc.B 38:54–59,1976.]entropy estimators using SRS,RSS,and DRSS schemes.It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.
