The standard boxplot is one of the most popular nonparametric tools for detecting outliers in univariate datasets. For Gaussian or symmetric distributions, the chance of data occurring outside of the standard boxplot fence is only 0.7%. However, for skewed data, such as telemetric rain observations in a real-time flood forecasting system, the probability is significantly higher. To overcome this problem, a medcouple (MC) that is robust to resisting outliers and sensitive to detecting skewness was introduced to construct a new robust skewed boxplot fence. Three types of boxplot fences related to MC were analyzed and compared, and the exponential function boxplot fence was selected. Operating on uncontaminated as well as simulated contaminated data, the results showed that the proposed method could produce a lower swamping rate and higher accuracy than the standard boxplot and semi-interquartile range boxplot. The outcomes of this study demonstrated that it is reasonable to use the new robust skewed boxplot method to detect outliers in skewed rain distributions.
On a Family of Discrete Log-Symmetric Distributions
