The Application Of Generalized Inference Method In Several Kinds Of Inference Problems

The generalized inference is a statistical inference method based on generalized test variables and generalized pivot quantities.Due to its good performance,it has been applied to various statistical inference problems in recent years.This paper discusses applications of generalized inference methods in parameter inference of several common distributions,including normal distribution,lognormal distribution,inverse gaussian distribution,multivariate normal distribution,exponential distribution,generalized inverse exponential distribution,etc.The main method adopted in this paper is to construct the fiducial model of interest parameters,obtain their generalized pivot quantities,and then give the generalized p values of the output test,as well as the generalized confidence interval of interest parameters.The main results are as follows:(1)Based on generalized inference,the difference between the mean values of two populations under normal distribution and exponential distribution are introduced,and the analytical solution of the generalized values of the hypothesis test problem is given.Then it is applied to the mean of truncated exponential distribution and the difference of the mean of measured truncated life test.(2)The applications of generalized inference in exponential distribution of single parameter and generalized inverse exponential distribution are given.For the single-parameter exponential distribution reliability parameter inference,the pivot equation is constructed and a new generalized pivot quantity of reliability parameter is given,and the frequency property of generalized confidence interval is proved.The confidence interval and its mean length,probability of making the first type error and the power of the test are given by monte Carlo simulation method,and then the method is compared with the bayesian method,the large sample method based on asymptotic normal and the Bootstrap resampling sampling method.This paper presents a statistical inference study of generalized inverse exponential distribution based on progressive type? deleted data and recorded data.Simulation results show that the generalized inference method has good frequency properties.(3)The statistical inference of the coefficient of variation and scale parameters of the inverse gaussian distribution is given.The generalized confidence interval of the coefficient of variation in the inverse gaussian distribution was given,and the method of variance of estimates recovery and Bootstrap method were compared.In addition,combining with the statistical properties of asymptotic normality,the correlation between the difference of each pair of scale parameters is eliminated to construct the simultaneous confidence interval,and the conclusion proves the good properties of the generalized inference method.(4)The problem of parameter inference of logarithmic normal population with the same mean value is studied,and the inference of interest parameters of multiple normal distributions is given.The simulation results prove the good properties of generalized inference method.