Recent Advances in Detecting Outliers in Moment Distributions

Abstract

The study of outliers is one of the challenges existed for at least several hundred years. Outliers are the observations which are stranger from the bulk of data. Sometimes outliers may not be noticed but most of the times they can change the entire statistical data analysis. At the earlier stage of the data analysis, summary statistics such as the sample mean and variance, outliers can cause totally different conclusion, e.g. a hypothesis may or may not be rejected due to outliers. In fitting regression line outliers can significantly change the slope and 2R . If the detection of outliers is not done properly before data analysis then it may lead to model misspecification, biased parameter estimation and incorrect results. It is therefore pertinent to identify the outliers prior to proceed further for analysis and modeling. Much work has been done in Univariate probability distributions. The objective of this study is to develop the methods which are used to detect the outliers in Univarite Moment Distributions. Two discordancy tests are developed to detect the single and two outliers from data characterized by Moment distributions. The exact distribution of developed tests does not exist, therefore for finding the Tables of critical values simulation study was used. The Tables of critical values are developed at 5% and 1% level of significance by means of a simulation study.Applications of two other methods which are based on sample skewness and Kurtoses have been extended to detect the outliers in Moment distributions. The Tables of critical values are also generated for these two methods at 5% and 1% level of significance on the basis of a simulation study. The performance rates of four methods are found at various sample sizes by means of a simulation study. It is worth mentioning that methods 𝐺1 and 𝐺2 only indicates the presence of outliers in the data, while methods 𝐷1 and 𝐷2 not only identify the presence of outliers but also specify the particular outliers.