|
In statistical graphics, the functional boxplot is an informative exploratory tool that has been proposed for visualizing functional data. Analogous to the classical boxplot, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve and the maximum non-outlying envelope. To construct a functional boxplot, data ordering is the first step. In functional data analysis, each observation is a real function, therefore, different from the classical boxplot where data are simply ordered from the smallest sample value to the largest, in a functional boxplot, functional data, e.g. curves or images, are ordered by a notion of band depth or a modified band depth. It allows for ordering functional data from the center outwards and, thus, introduces a measure to define functional quantiles and the centrality or outlyingness of an observation. Having the ranks of functional data, the functional boxplot is a natural extension of the classical boxplot. ==Construction== In the classical boxplot, the box itself represents the middle 50% of the data. Since the data ordering in the functional boxplot is from the center outwards, the 50% central region is defined by the band delimited by the 50% of deepest, or the most central observations. The border of the 50% central region is defined as the envelope representing the box in a classical boxplot. Thus, this 50% central region is the analog to the "interquartile range" (IQR) and gives a useful indication of the spread of the central 50% of the curves. This is a robust range for interpretation because the 50% central region is not affected by outliers or extreme values, and gives a less biased visualization of the curves' spread. The observation in the box indicates the median, or the most central observation which is also a robust statistic to measure centrality. The "whiskers" of the boxplot are the vertical lines of the plot extending from the box and indicating the maximum envelope of the dataset except the outliers. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「functional boxplot」の詳細全文を読む スポンサード リンク
|