Research On Some Problems Of Statistical Inference For The Model Of Recorded Data Occasions

Record value theory is closely related to our production and life. In recent years, the recorded value model on the occasion of the data has been widely stud-ied and applied. This paper discussed record value data cases model parameters estimation problem, mainly to study the following aspects:First of all, in the recorded value under the situation of sample data, this pa-per discusses the estimation of parameters of two parameter exponential Weibull model. Bayesian estimation is obtained in the case that the conjugate prior dis-tribution of the parameter is Gamma prior distribution and the loss function is quadratic error loss and LINEX loss function. Because of the complexity of the estimation, an approximate method is presented to obtain the analytical form, and the deviation and mean square error of Bayesian estimation and maximum likelihood estimation are compared by numerical simulation. The results show that in proper prior distribution under the condition of Bayes estimation values are more close to the true parameter values.Secondly, according to the record value samples, the Rayleigh distribution model is selected to study the parameter estimation of reliability index. Esti-mation of reliability index Bayes Rayleigh reliability index and the maximum likelihood estimation is given in this paper at first, then in the loss function for the case of squared error loss derived distribution, using R software for numerical simulation, and compare the two parameter estimation error and mean square er-ror found under symmetric loss function Bayes of reliability index estimate value is better than the maximum likelihood estimation.Finally, on the basis of previous research, this paper selects the two parame-ter exponential Weibull model, record samples to discuss the interval estimation. Using R software to carry on the numerical simulation, respectively, and the ap-plication of the approximate confidence intervals based on, based on bootstrap method of confidence interval estimation and bilateral Bayesian probabilistic con-fidence intervals for the three methods are compared and analyzed, finally draws the conclusion:Bayesian probability confidence interval estimates are obtained.