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
In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive type-I interval censoring. The Bayesian estimates of p...In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive type-I interval censoring. The Bayesian estimates of parameters and reliability function cannot be obtained as explicit forms by applying squared error loss and Linex loss functions, respectively; thus, we present the Lindley＇s approximation to discuss these estimations. Then, the Bayesian estimates are compared with the maximum likelihood estimates by using the Monte Carlo simulations.展开更多
In this article,we consider the statistical inferences of the unknown parameters of a generalized inverted exponential distribution based on the Type II progressively hybrid censored sample.By applying the expectation...In this article,we consider the statistical inferences of the unknown parameters of a generalized inverted exponential distribution based on the Type II progressively hybrid censored sample.By applying the expectation–maximization(EM)algorithm,the maximum likelihood estimators are developed for estimating the unknown parameters.The observed Fisher information matrix is obtained using the missing information principle,and it can be used for constructing asymptotic con-fidence intervals.By applying the bootstrapping technique,the confidence intervals for the parameters are also derived.Bayesian estimates of the unknown parameters are obtained using the Lindley’s approximation.Monte Carlo simulations are imple-mented and observations are given.Finally,a real data set representing the spread factor of micro-drops is analyzed to illustrative purposes.展开更多
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Supported by the National Natural Science Foundation of China (No. 11161031)Natural Science Foundation of Inner Mongolia (2010MS0116)Higher school science and technology research project of Inner Mongolia (NJ10085)
文摘In this study, we consider the Bayesian estimation of unknown parameters and reliability function of the generalized exponential distribution based on progressive type-I interval censoring. The Bayesian estimates of parameters and reliability function cannot be obtained as explicit forms by applying squared error loss and Linex loss functions, respectively; thus, we present the Lindley＇s approximation to discuss these estimations. Then, the Bayesian estimates are compared with the maximum likelihood estimates by using the Monte Carlo simulations.
文摘In this article,we consider the statistical inferences of the unknown parameters of a generalized inverted exponential distribution based on the Type II progressively hybrid censored sample.By applying the expectation–maximization(EM)algorithm,the maximum likelihood estimators are developed for estimating the unknown parameters.The observed Fisher information matrix is obtained using the missing information principle,and it can be used for constructing asymptotic con-fidence intervals.By applying the bootstrapping technique,the confidence intervals for the parameters are also derived.Bayesian estimates of the unknown parameters are obtained using the Lindley’s approximation.Monte Carlo simulations are imple-mented and observations are given.Finally,a real data set representing the spread factor of micro-drops is analyzed to illustrative purposes.
