In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy di...In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.展开更多
设{Xk,1≤ k ≤n}独立同分布,X(1),X(2),······ X(n)为其顺序统计量,当总体服从Kum(λ,φ)分布时,得到了其顺序统计量的联合概率密度、极端值顺序统计量的概率密度和k阶矩的表达式.此外还研究了极端值顺...设{Xk,1≤ k ≤n}独立同分布,X(1),X(2),······ X(n)为其顺序统计量,当总体服从Kum(λ,φ)分布时,得到了其顺序统计量的联合概率密度、极端值顺序统计量的概率密度和k阶矩的表达式.此外还研究了极端值顺序统计量X(1)和X(n)的渐近分布。展开更多
为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特...为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)方法给出参数及应力-强度模型可靠度的贝叶斯估计;最后,利用逆矩估计方法给出参数及应力-强度模型可靠度的逆矩估计(inverse moment estimation,IME)。数值模拟结果表明,在不同系统可靠度及不同样本量条件下,通过对3种估计方法的数值进行比较发现贝叶斯估计效果最好,IME优于MLE。该研究为探讨串联系统多部件应力-强度模型可靠性提供了一定的理论基础。展开更多
The techniques to find appropriate new models for data sets are very popular nowadays among the researchers of this area where existed models in the literature are not suitable. In this paper, a new distribution, gene...The techniques to find appropriate new models for data sets are very popular nowadays among the researchers of this area where existed models in the literature are not suitable. In this paper, a new distribution, generalized inverted Kumaraswamy (GIKum) distribution is introduced. The main aims of this research are to develop a general form of inverted Kumaraswamy (IKum) distribution which is flexible than the IKum distribution and all of its related and sub models. Some properties of GIKum distribution such as measures of central tendency and dispersion, models of stress-strength, limiting distributions, characterization of GIKum distribution and related probability distributions through some specific transformations are derived. The mathematical expressions of reliability function (r.f) and the hazard rate function (hrf) of the GIKum distribution are found and presented through their graphs. The parameters estimation through the maximum likelihood (ML) estimation method is used and the results are applied to the data set of prices of wooden toys of 31 children.展开更多
In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type...In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.展开更多
In reliability theory,the reliability inference for s-out-of-k systems holds significant importance.In this paper,we explore the estimation of reliability for s-out-of-k systems based on partially constant stress acce...In reliability theory,the reliability inference for s-out-of-k systems holds significant importance.In this paper,we explore the estimation of reliability for s-out-of-k systems based on partially constant stress accelerated life tests.Assume that the latent failure times of the components follow the Kumaraswamy distribution.Maximum likelihood estimates for the unknown parameters are established,and their uniqueness is demonstrated.In addition,confidence intervals for the unknown parameters are constructed using the covariance matrix.Confidence intervals for the reliability functions are determined by the Delta method,while Bootstrap intervals are provided for comparison purposes.Subsequently,Bayesian point and interval estimates based on MCMC techniques considering different loss functions are discussed.Lastly,we conduct an extensive simulation study and analyse one real data set,which reveals that the Bayesian approach yields the best results.展开更多
基金funded by Researchers Supporting Project number(RSPD2025R969),King Saud University,Riyadh,Saudi Arabia.
文摘In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.
文摘为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)方法给出参数及应力-强度模型可靠度的贝叶斯估计;最后,利用逆矩估计方法给出参数及应力-强度模型可靠度的逆矩估计(inverse moment estimation,IME)。数值模拟结果表明,在不同系统可靠度及不同样本量条件下,通过对3种估计方法的数值进行比较发现贝叶斯估计效果最好,IME优于MLE。该研究为探讨串联系统多部件应力-强度模型可靠性提供了一定的理论基础。
文摘The techniques to find appropriate new models for data sets are very popular nowadays among the researchers of this area where existed models in the literature are not suitable. In this paper, a new distribution, generalized inverted Kumaraswamy (GIKum) distribution is introduced. The main aims of this research are to develop a general form of inverted Kumaraswamy (IKum) distribution which is flexible than the IKum distribution and all of its related and sub models. Some properties of GIKum distribution such as measures of central tendency and dispersion, models of stress-strength, limiting distributions, characterization of GIKum distribution and related probability distributions through some specific transformations are derived. The mathematical expressions of reliability function (r.f) and the hazard rate function (hrf) of the GIKum distribution are found and presented through their graphs. The parameters estimation through the maximum likelihood (ML) estimation method is used and the results are applied to the data set of prices of wooden toys of 31 children.
基金supported by the Natural Science Foundation of Guangdong(No.2024A1515010983)the project of Guangdong Province General Colleges and Universities with Special Characteristics and Innovations(No.2022KTSCX150)+2 种基金Zhaoqing Science and Technology Innovation Guidance Project(No.2023040317006)Zhaoqing Institute of Education Development Project(No.ZQJYY2023021)Zhaoqing College Quality Project and Teaching Reform Project(No.zlgc202112).
文摘In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.
基金supported by the National Natural Science Foundation of China[grant number 12361060]Funds for Innovative Fundamental Research Group Project of Gansu Province[grant number 23JRRA684]College Teachers Innovation Foundation Project of Gansu Provincial Education Department[grant number 2024A-002].
文摘In reliability theory,the reliability inference for s-out-of-k systems holds significant importance.In this paper,we explore the estimation of reliability for s-out-of-k systems based on partially constant stress accelerated life tests.Assume that the latent failure times of the components follow the Kumaraswamy distribution.Maximum likelihood estimates for the unknown parameters are established,and their uniqueness is demonstrated.In addition,confidence intervals for the unknown parameters are constructed using the covariance matrix.Confidence intervals for the reliability functions are determined by the Delta method,while Bootstrap intervals are provided for comparison purposes.Subsequently,Bayesian point and interval estimates based on MCMC techniques considering different loss functions are discussed.Lastly,we conduct an extensive simulation study and analyse one real data set,which reveals that the Bayesian approach yields the best results.
