Fiducial Inference And Gamma Distribution Parameter Test Related Research

In actual production and life,Gamma distribution has been widely used in many fields,such as reliability,survival analysis and infectious disease research,engineering,hydrology,meteorology and so on.Therefore,it is of practical significance to study the interval estimation of the ratio of the parameters of the Gamma distribution and the hypothesis test of the parameters based on the Fiducial inference in this paper.In this paper,the Fiducial method is used to construct the confidence interval of the ratio of the parameters and the ratio of the mean of the two populations in the Gamma distribution,and monte carlo simulation is used to simulate the confidence interval,so as to obtain the coverage rate and draw the box diagram of the interval length.The hypothesis testing of the parameters of a Gamma distribution population is studied.Firstly,the existing methods for this problem are introduced,including SBT,CAT and TGPT.In this paper,a p-value calculation method is proposed to solve this problem,and the numerical simulation comparison between this method and the previously introduced method is carried out under different conditions.According to the results,it can be seen that this method has great advantages in approaching significance level.