In this paper, we give a definition of the alternating iterative maximum likelihood estimator （AIMLE） which is a biased estimator. Furthermore we adjust the AIMLE to result in asymptotically unbiased and consistent ...In this paper, we give a definition of the alternating iterative maximum likelihood estimator （AIMLE） which is a biased estimator. Furthermore we adjust the AIMLE to result in asymptotically unbiased and consistent estimators by using a bootstrap iterative bias correction method as in Kuk （1995）. Two examples and simulation results reported illustrate the performance of the bias correction for AIMLE.展开更多
Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated...Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.展开更多
We consider the maximum likelihood estimator of the unknown parameter in aclass of nonstationary diffusion processes. We give further a precise estimate for the error of theestimator.
基金Supported by the National Natural Science Foundation of China(Grant Nos.7117103571173029+3 种基金1093100211071035)the Program for New Century Excellent Talents(Grant No.NCET-10-315)Excellent TalentsProgram of Liaoning Educational Committee(Grant No.2008RC15)
文摘In this paper, we give a definition of the alternating iterative maximum likelihood estimator （AIMLE） which is a biased estimator. Furthermore we adjust the AIMLE to result in asymptotically unbiased and consistent estimators by using a bootstrap iterative bias correction method as in Kuk （1995）. Two examples and simulation results reported illustrate the performance of the bias correction for AIMLE.
文摘Mixtures of lifetime distributions occur when two different causes of failure arc present, each with the same parametric form of lifetime distributions. This paper is considered with the mixture model of exponentiated Rayleigh and exponentiated exponential distributions. The author＇s objectives are finding the statistical properties of the model and estimating the parameters of the model by using point estimation and interval estimation methods. First, some properties of the model with some graphs of the density function are discussed. Next, the maximum likelihood method of estimation is used for estimating scale and shape parameters of the model. Estimating the parameters is studied under complete and type II censored samples for different sample sizes. Asymptotic Fisher information matrix of the estimators for complete samples is founded with different sample sizes. The asymptotic variances of the maximum likelihood estimates are derived. Based on the asymptotic variances of the maximum likelihood estimates, interval estimates of the parameters are obtained. Some of the equations in this paper are solved by using numerical iteration such as Newton Raphson method by using Mathematica 7.0. The performance of findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation study based on absolute relative bias and mean square error.
基金Research partially supported by N.S.F.Grants DMS-0203823Doctoral Program Foundation of the Ministry of Education of China,Grant No.20020269015
文摘We consider the maximum likelihood estimator of the unknown parameter in aclass of nonstationary diffusion processes. We give further a precise estimate for the error of theestimator.
