Statistical Detection Of The Abnormal Observations

This paper investigates the statistical detection method for outliers in the observational data. Concerning several important distributional population about the reliability theory, such as Exponential Distribution, Two-Parameter Exponential Distribution, Two-Parameter Weibull Distribution, Extreme Value Distribution.The detection method is discussed if multiple outliers occur in the sample observational data. Several new preferable test statistics based on the order statistic or the superior estimate of the parameter are given.This paper discusses the detection efficiency by theoretical analysis.The analysis shows these detection methods can avoid the interference such as the swamping effect or the masking effect because of the existence of multiple outliers.In the first chapter, a brief introduction is given to describe the research background, recent situation and application instances of the detection for outliers.In the second chapter, the Z -type test statistic~[51] for detecting multiple outliers from the Exponential Distribution is analysed.The paper derives the large sample distribution of the Z -type test statistic and presents the approximate representation of the critical value. Concerning Type-I censored sample from the Exponential Distribution, the detection method is given if there are many upper outliers and many lower outliers in the sample.In the third chapter, concerning multiple outliers from the sample of the Two-Parameter Weibull Distributio, a new detection method is given.The sample fractile and the equivariant estimators of the scale parameter of the I -Type Extreme Value Distribution is used to construct the new test statistic.This paper discusses the detection efficiency.The discussion indicates the test statistic can avoid the masking effect.We can use the transformation of the new test statistic to detect multiple outliers from the I -Type Extreme Value Distribution.In the fourth chapter, concerning multiple outliers from the sample of the Two-Parameter Exponential Distribution, a new detection methods is given. This paper constructs a new test statistic based on the superior estimate of the parameter. This paper derives the accurate density function and the large sample approximate distribution of the test statistic.This paper discusses the detection efficiency.The discussion indicates the test statistic can avoid the masking effect.