Research On The Test Method Of Outliers Based On Statistical Theory

Outlier is the individual value in a batch of data and its value deviate significantly from the rest of the observations.The existence of outliers will increase the error of analysis results,and make some classical statistical analysis methods useless,and even lead to the error of overall decision-making,causing inestimable losses.Therefore,how to test these outliers is an important practical problem.Outlier testing is to test some outliers whether are in a group of samples or not,and then find out the location of the outliers.In this paper,statistical theory is used to test outliers in the observational data.Concerning several common distribution of location-cale parameter,such as Extreme Value Distribution,Exponential Distribution,Two-Parameter Exponential Distribution,testing their outliers is studied in detail.The proper test statistics are constructed by using the order statistic or the superior estimate of the parameter,so as to build a new test method.Its main results are as follows:Firstly,this paper discussed the testing outliers from the Extreme Value Distribution,and defined the contribution rate of order statistics,and utilized best linear unbiased estimates(BLUE)of the scale parameter ? to construct test statistics.And then,the paper obtains the quantiles of test statistics disribution through Monte-Carlo simulations,and the suspected number of outliers is given.At the end of this chapter,an example is employed to illustrate the feasibility of the proposed method.Secondly,this paper discussed the testing outliers from the Exponential Distribution,?k is estimated by using mean rate ? of the order statistics.Based on the jump degree of ?k the test statistics are constructed by using the volatility.And the specific test method for abnormal data is given.At the end of this chapter,an example is employed to illustrate the feasibility of the proposed method.Finally,this paper discussed the procedures of testing outliers from the Two-Parameter Exponential Distribution,by using the robustness of sample quantile and based on the asymptotic unbiased,consistent estimation of the parameter,the test statistic is constructed,and derived the accurate density function and the approximate distribution of test statistics,which provides the basis for the critical value of testing.