Testing On Upper And Lower Outliers In Two-parameter Weibull Samples

The problem of the quality of statistical data not only continuously puzzles the national statists, but also receives the attentions from all circles. So the research on the theory maintains hot recently. The essence of the problem affecting the quality of statistical data is the error caused mainly by the outliers, so eliminating the outliers is the most important.Although the cognitions on outliers are different to different person, generally speaking, there're two kinds-broad sense and narrow sense. For some reasons, the scholars pay more attention on the testing of the narrow ones. The narrow outliers also called stray datas, which are different from others obviously. The outliers also can divide into two kinds-pper outliers and lower outliers.In this paper, we discuss the problem of testing the data with upper outliers and lower outliers in two-parameter Weibull examples, basing on the MLE of the parameters. At first, a new statistic and its exact distribution are given when m is known, then we extend the statistic to apply to the situation when m is unknown, and give its percentile values by Monte-Carlo method. As a result, the problem of testing the outliers in two-parameter Weibull examples is solved primely.