On Statistical Inference Of Coefficient Of Variation Ratio Of Gamma Distribution

As an important indicator of data dispersion,coefficient of variation has been widely used in environmental monitoring,economy and finance,industrial health,genetic research and quality control,and the data in these fields have obvious right deviation characteristics,which can be approximately fitted by gamma distribution.The ratio of the two groups of data corresponding to the coefficient of variation can reflect the differences in different environmental control measures,product quality control methods,experimental variable improvement and other aspects,and provide some guidance for enterprises and governments to achieve better production efficiency and technology optimization.Therefore,the interval estimation of the coefficient of variation ratio of two gamma distributions has become a research hotspot of many experts and scholars.Although the point estimator is a very useful statistic,the confidence interval is more conservative,which can provide us more information about the parameters of interest.In this dissertation,for the interval estimation of the ratio of variation coefficients of two independent gamma distributions,we construct a method to solve the confidence interval based on the Fiducial inference.Considering the constraints in the application environment,we further study the interval estimation of the ratio of variation coefficients under the condition of bounded parameters.Then,taking the coverage,average length,left error rate and right error rate of confidence interval in Monte Carlo simulation as comparison indexes,the performance of interval estimation method based on fiducial inference is compared with that based on variance estimation restoration method(MOVER),Wald interval and Score interval,In the hypothesis test,the probability of making the first type of error and the efficacy value are used as indicators to compare the effects of the three statistical tests.Finally,it is concluded that the interval estimation method based on fiducial inference performs better than the other two methods in most cases,with high coverage,the shortest interval length,and balanced left and right error rates,especially in the case of small samples and two different sample sizes.Finally,the three interval estimation methods are applied to the data of continuous time between failures of aircraft and daily average PM2.5 content in Thailand,and the results show that they have good applicability.