Outlier Detection Using Power Mean

Outliers have been regarded as the noisy data in statistics which have now turned out to be an important problem and are now been researched in diverse fields and application domains. Outlier detection has been in core interest of not only the statisticians but all the professionals who are working on a particular data set. Many outlier detection techniques have been developed specific to certain application domains, while some techniques are more generic. This work has added one more technique to the bucket list of all those professionals. Power mean which has been used as a general method to calculate various means like arithmetic mean (power mean with power 1), geometric mean (power mean with power 0), Lorentz mean (power mean with power 1/3) etc. can also be used to detect the sensitivity of the data towards being the outlier. This work studies various powers of power mean for outlier detection. It contains two different data sets, one containing fractions and the other integers. The results have been verified by the existing standard techniques of outlier detection. Thus this book contains description of detecting outliers using power mean with different types of data sets, graphs and figures for better understanding. The idea is to check the efficacy of the method using a data set in which the outlier or the anomaly is already known and then testing the same method for a data set in which the outliers are not known to us. The open research issues and challenges at the end will provide researchers a clear path for the future of outlier detection methods.