Statistical Inference For Record Value And Record Ranked Set Sampling Scheme

Record value as a common form of data,has been widely used in the field of meteorology,hydrology,sports and life test.For example,in hydrology,the rainfall during the same period in each year appears in the form of record value;in sports a record value is constantly being refreshed.Record value is a special form of order statistics.With the development of research on the ranked set sampling,a lot of sampling schemes based on ranked set sampling are derived.Based on the recorded value,a new ranked set sampling scheme is proposed and called record ranked set sampling scheme(RRSS).In this thesis,we discuss the problem of statistical inference for record value and record ranked set sampling scheme:(1)Based on record value,the point estimation and confidence interval estimation of the parameters are discussed under the extreme value distribution model.On the point estimation problem,the maximum likelihood estimation and inverse moment estimator are derived.On the interval estimation problem,we discuss the asymptotic confidence intervals and accurate confidence intervals.When establishing the accurate confidence intervals of parameters,we discuss the construction method of2? distribution and F distribution respectively,and discuss the pivot under the two methods with the existence and uniqueness of solution.Finally,a specific example is proposed.(2)Based on record ranked set sampling scheme,the maximum likelihood estimation of Weibull distribution is obtained.Under the asymptotic normality of the maximum likelihood estimate,the asymptotic confidence intervals of parameters are investigated,we also discuss the interval estimation of parameters under the bootstrap method.In Bayesian analysis,the Jeffreys and Reference priors are considered as the non-information prior to infer the parameters from the objective Bayesian analysis.Since the numerical solution of the Bayesian estimation of parameters can not beobtained directly,the Metropolis-Hastings algorithm and Gibbs sampling are used to solve the problem.Finally,the Monte-Carlo numerical simulation is used to compare the methods discussed.