Statistical Inference Problems With The Normal Mean When The Coefficient Of Variation Is Known

The research on normal mean with known coefficient of variation appears in the fields of environmental science,clinical chemistry and pharmaceutical science.With the continuous development of these fields,more and more attention has been paid to this research problem.The data of this kind of research are mostly obtained by experiments,and the data sample size is often small.Therefore,the effective methods to solve this kind of problem for small sample data are concerned.Considering the advantages of Fiducial inference method in solving the problem of small sample parameter model in recent years,this dissertation uses Fiducial inference method to study the interval estimation of the mean value of a single population and the difference between two populations under the assumption that the population comes from normal distribution and the coefficient of variation is known,this dissertation also uses the generalized p-value method to test the mean value.The author proposes a Fiducial generalized pivot quantity to solve the normal mean value when the coefficient of variation is known.The interval constructed by the new pivot quantity is compared with the interval constructed by a known pivot quantity.From the three aspects of interval coverage probability,average interval length and the left and right error rate of the interval,the interval constructed by the proposed Fiducial generalized pivot quantity has better performance in the case of large samples and small samples.In this dissertation,we use the generalized p-value as a test statistic to test the mean value of a single normal distribution population when the coefficient of variation is known.We test the type one error rate as well as power of two-sided test and one-sided test by Monte Carlo simulation.At the same time,this dissertation estimates the mean difference of two normal populations with known coefficient of variation.In this dissertation,three intervals are constructed.One is based on the method of Fiducial inference,the Fiducial generalized pivot quantity is obtained to calculate the mean difference between two populations,and then the interval of mean difference is constructed;The other two intervals are obtained by Parametric Bootstrap(PB)method based on different estimators.The three confidence intervals are compared with two traditional confidence intervals and an interval constructed by method of variance of estimates recovery(MOVER).In addition,noise is added to compare the robustness of the interval constructed by each method,and the computational efficiency of each interval construction method is also demonstrated.After a series of comprehensive comparisons,the interval obtained by Fiducial inference method performs better,especially in the case of small samples,which is recommended to be used in practice.In this dissertation,the generalized p-value method is also used to test the hypothesis of the comparison of the mean values of two normal populations with known coefficient of variation.The Fiducial generalized pivot quantity of the mean difference and a generalized pivot quantity based on PB method are used as test statistics.The type one error rate and power of two tests are compared,numerical simulation shows that the type one error rate based on the Fiducial generalized pivot quantity is closer to the nominal level and has higher power.