Modified boxplot and stairboxplot for generalized extreme value distribution

A boxplot is an exploratory data analysis tool for a compact distributional summary of a univariate dataset. It is designed to recognised all typical observations and displays the location, spread, skewness and the tail of the data. When the dataset is skewed such as extreme data, the precision of boxplot functionalities is less reliable and inaccurate. Many observations from extreme data were erroneously marked as outliers by the classical boxplot methods. The Tukey’s classical and Hubert’s adjusted boxplots were utilize in the study based on outside rate per sample and a propose measure of fence sensitivity ratio to observe the suitability of the methods according to a simulation process from Generalized Extreme Value distribution. The adjusted method improves the classical method in extreme data capture but not sufficiently optimize to achieve the bench mark requirement in the literature. The modified boxplot has been proposed with a fence adjustment of the existing boxplot method using the Bowley coefficient. The fence position was considered as a response to skewness in the simulated extreme data from GEV distribution and then fitted with resistance fit linear regression model. The propose fence adjustment enhance the boxplot to detect all atypical observations without any parametric assumption about an extreme data. The new boxplot displays some additional features other than the classical one such as a quantile region for the parameters of Generalized Extreme Value distribution in fitting an extreme data. The modification of the entire boxplot display is also proposed as stairboxplot with combined features of boxplot, histogram and a dot plot. The stairboxplot divides the data points of a sample into four portions according to the range of the data set, such that the individual points are inscribed in their respective range levels. However, stairboxplot displays each observation according to an introduce measure of outlyingness of a point called stairboxplot outlyingness. The main findings and contributions in both modified boxplot and stairboxplot can generally be attributed to the enhancement of quality of a dataset by highlighting inconsistent observations from GEV distribution’s modelling framework and diagnostic visualisation of extreme data to gain immediate information such as skewness, quantile estimate of GEV parameters region and data points display according to outlyingness.

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