A New Method of Processing Outliers in Measurement

摘要

This paper presents a method to process measured outliers. Through measurement we often get plenty of data that provides information about events. We define information in three kinds: effective information, useful information and bad information. Effective information tells the sample distribution mode of measurement data correctly, useful information reflects basic characters of the sample distribution, and bad information will disturb correct estimation. So we must restrict bad information, even get it out. For instance, outlier is bad information in measurement. Early in the first years of 19 century, robust estimation was used to cut down outliers. But there was less interest in robust estimation until computer technology had great development. The principles of robust against outliers are fully using effective information, considering useful information and forbidding bad information. Robust least square estimation can deal with the sample distribution, whose main body is normal distribution but contaminated by outliers. There are many sample distributions that do not fit normal distribution but fit other distributions in practice. The advantage of Beta distribution is that it includes other kinds of distributions. The proposed method can deal with measured data fitting not only contaminated normal distribution but also other distributions by applying the robust estimation based on Beta distribution.