The surface boxplot is a natural extension of the functional boxplot to R 3.However, there are a series of Boxplot variations that can display the distribution of data over two, three or even more dimensions. Any surface outside the fences are flagged as outlier candidates. Similarly, the fences are obtained by the 1.5 times the 50% central region rule. In the latter case, a volume-based surface band depth can be used to order sample surfaces and leads to a three-dimensional surface boxplot with similar characteristics as the functional boxplots. Spatio-temporal data can be viewed as a temporal curve at each spatial location, or a spatial surface at each time. When each observation is simply a point, the functional boxplot degenerates to a classical boxplot, and it is different from the pointwise boxplots.īy introducing the concept of central regions, the functional boxplot can be generalized to an enhanced functional boxplot where the 25% and 75% central regions are provided as well. Any observations outside the fences are flagged as potential outliers. ![]() The fences are obtained by inflating the envelope of the 50% central region by 1.5 times the ![]() Outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the 1.5 IQR empirical rule for classical boxplots. The "whiskers" of the boxplot are the vertical lines of the plot extending from the box and indicating the maximum envelope of the The observation in the box indicates the median, or the most central observation which is also a robust statistic to measure centrality. Less biased visualization of the curves' spread. This is a robust range for interpretation because the 50% central region is not affected by outliers or extreme values, and gives a Region is the analog to the " interquartile range" (IQR) and gives a useful indication of the spread of the central 50% of the curves. Theīorder of the 50% central region is defined as the envelope representing the box in a classical boxplot. 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. ![]() In the classical boxplot, the box itself represents the middle 50% of the data. Having the ranks of functional data, the functional boxplot is a natural extension of the classical boxplot. 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. curves or images, are ordered by a notion of band depth or a modified band depth. 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. To construct a functional boxplot, data ordering is the first step. ![]() 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. In statistical graphics, the functional boxplot is an informative exploratory tool that has been proposed for visualizing functional data.
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