Multiple Comparison Test Of Coefficient Of Variation Of Gamma Distribution Based On Two-sample Bootstrap Test

The gamma distribution is a popular distribution model,which is suitable for mod-eling data with right-skewness and is widely used in climatology,finance and environ-mental science.The common estimators of gamma distribution are moment estimation and maximum likelihood estimation.The moment estimation of gamma distribution has a large deviation,while the maximum likelihood estimation does not show an ex-pression.The maximum likelihood estimation mainly adopts iterative or Monte Carlo simulation.The closed-form estimators for the gamma distribution are derived from the likelihood equations of generalized gamma distribution.The closed-form estimator has a display expression,and its deviation and root mean square error are equivalent to the case corresponding to the maximum likelihood estimator.Coefficient of variation is a normalized measure to describe the dispersion degree of random variable.It is the ratio of the standard deviation of random variable to the mean.In this paper,accord-ing to the asymptotic property of the closed-form estimator,the closed-form estimator of the coefficient of variation follows the normal distribution asymptotically,and then the difference of the closed-form estimator of the coefficient of variation under two samples follows the normal distribution asymptotically.On this basis,the two-sample Bootstrap test and two-sample parametric Bootstrap test were constructed,and the con-clusion that the test power was improved under small samples was obtained through power simulation.By HH-0 stepwise upward multiple comparison test,the two-sample test is extended to multiple samples,and the multiple comparison test of the coefficient of variation of the gamma distribution is performed.The power simulation of multiple test for equality of coefficient of variation was carried out under three-sample,and the simulation results show that the test method is feasible.We further studied whether the coefficient of variation of each region in the spatial grid region was different from that of the region adjacent to the spatial position of the region,and Bootstrap method was used to explore the global test of the coefficient of variation of adjacent space.The empirical analysis used the number of serious crime and misdemeanor committed in the total of 72 months from 2008 to 2013 in nine city council districts in Pittsburgh and the daily air quality index data for all cities in Anhui province in 2019,which further verified the applicability of the multiple comparison test of the coefficient of variation of the gamma distribution and global test of coefficient of variation in adjacency space.