Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditio...Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.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 article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distri...In this article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility for modeling lifetime data.The new distribution includes the inverse Lindley and the Marshall-Olkin inverse Lindley as special distributions.Essential properties of the generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated including,quantile function,ordinary moments,incomplete moments,moments of residual and stochastic ordering.Maximum likelihood method of estimation is considered under complete,Type-I censoring and Type-II censoring.Maximum likelihood estimators as well as approximate confidence intervals of the population parameters are discussed.A comprehensive simulation study is done to assess the performance of estimates based on their biases and mean square errors.The notability of the generalized Marshall-Olkin inverse Lindley model is clarified by means of two real data sets.The results showed the fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits than power Lindley,extended Lindley,alpha power transmuted Lindley,alpha power extended exponential and Lindley distributions.展开更多
基金This work was funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under Grant No.FP-190-42.
文摘Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress,such as pressure,temperature,vibration,voltage,or load to induce early failures.In this paper,a step stress partially accelerated life test(SSPALT)is regarded under the progressive type-II censored data with random removals.The removals from the test are considered to have the binomial distribution.The life times of the testing items are assumed to follow lengthbiased weighted Lomax distribution.The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax.The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix.The Bayesian estimators cannot be obtained in the explicit form,so the Markov chain Monte Carlo method is employed to address this problem,which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters.The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations.In addition,to compare the performance of the considered confidence intervals for different parameter values and sample sizes.The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter,for different sample sizes,observed failures,and censoring schemes,in most cases.Also,the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes,observed failures,and censoring schemes,in most cases.Further performance comparison is conducted by the experiments with real data.
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.
基金This project was funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under grant No.(DF-279-150-1441).The authors,therefore,gratefully acknowledge DSR technical and financial support.
文摘In this article,a new generalization of the inverse Lindley distribution is introduced based on Marshall-Olkin family of distributions.We call the new distribution,the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility for modeling lifetime data.The new distribution includes the inverse Lindley and the Marshall-Olkin inverse Lindley as special distributions.Essential properties of the generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated including,quantile function,ordinary moments,incomplete moments,moments of residual and stochastic ordering.Maximum likelihood method of estimation is considered under complete,Type-I censoring and Type-II censoring.Maximum likelihood estimators as well as approximate confidence intervals of the population parameters are discussed.A comprehensive simulation study is done to assess the performance of estimates based on their biases and mean square errors.The notability of the generalized Marshall-Olkin inverse Lindley model is clarified by means of two real data sets.The results showed the fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits than power Lindley,extended Lindley,alpha power transmuted Lindley,alpha power extended exponential and Lindley distributions.
