Statistical Inference For The Comparison Of Two Populations In Several Types Of Situations

The Fieller problem has always been important in the field of technological development and research.Therefore,the Fieller problem has become a hot issue in research.The Fieller problem is more common in the bioequivalence test,but the bioequivalence test involves the inference of the population mean,and the inference of the coefficients of the multiple linear regression model.Many scholars have given statistical inference methods for the above problems.But many scholars are still focus on finding a more accurate and stable statistical inference program to solve the above problems.This paper mainly makes statistical inferences on the ratio of two population in several cases.Firstly,we performed a statistical inference for the ratio of two population means from normal distributions under the same variance and heteroscedasticity,respectively.The generalized fiducial inference method(GFCI)and the parametric bootstrap method(BCI)are used to give the generalized pivotal quantities of the ratio of two population means,and the generalized confidence intervals are constructed based on the generalized pivotal quantities.Monte Carlo simulation results show that the parameter bootstrap method(BCI)performs well under the same variance.Furthermore,the interval coverage and interval length perform well under the large sample size.The generalized fiducial inference method(GFCI)has good coverage in both cases.And the confidence interval of the generalized fiducial inference method(GFCI)is still stable and accurate under different variables,which shows that the generalized fiducial inference method(GFCI)has a wide application range.Secondly,we make statistical inference of the coefficients of the multiple linear regression model.The generalized pivot quantities of the ratio of two regression coefficients are given by the generalized fiducial inference method under the different cases of different intercepts and common intercepts.And the generalized confidence interval is given by the generalized pivot quantities.Under the different cases of different intercepts and common intercepts,Monte Carlo simulation results show that the generalized confidence intervals constructed by the generalized fiducial inference method have good interval coverage and interval length.Finally,we summarize and evaluate the statistical inference methods of the ratio of two normal population means and the ratio of the two regression coefficients,and analyze the simulation results.In addition,this paper points out the future work.