Research And Comparison Of Belief Inference Of Inverse Gamma Distribution

Inverse gamma distribution is an important statistical distribution,which is widely used in physics,medicine,aviation,biology and other fields.In this paper,fiducial inference is extended to the study of inverse gamma distribution.The problem of finding confidence limits for the mean,parameters and an upper percentile scale of inverse gamma distribution and are considered.In censored case,confidence limits for the mean and parameters have also been inferred.According to the characteristics of inverse gamma distribution and the common methods of interval estimation,fiducial interval estimation method of parameter and mean based on negative cube root transformation,Bayesian interval estimation of scale parameters with known shape parameters,bootstrap interval estimation of scale parameters based on maximum likelihood estimation and three methods of depending on pivot value are studied.Monte Carlo simulation studies indicate that fiducial interval results for quintiles of inverse gamma distribution are accurate in uncensored case.And the interval estimation results of parameters of inverse gamma distribution are not good in the case of missing.In addition,the coverage of fiducial interval estimation and bootstrap interval estimation based on maximum likelihood estimation is close to the nominal level.Compared with the interval estimation of the mean value of the inverse gamma distribution,the average interval length obtained by the Bayesian interval estimation method is the smallest in the case of small samples,the average interval length obtained by the interval estimation method of constructing pivots through the properties of the gamma distribution is the largest,and the interval estimation method based on the autocovariance estimation is the most unstable.In terms of coverage,when the shape parameter is large,the coverage of fiducial interval of inverse gamma distribution is closest to the nominal level.In the actual data,we should consider the actual situation and the advantages and disadvantages of each method,and choose the most suitable interval estimation method.