Functional boxplots

Ying Sun*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

320 Scopus citations


This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward ordering induced by band depth for functional data, 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 addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. This article has supplementary material online.

Original languageEnglish (US)
Pages (from-to)316-334
Number of pages19
Issue number2
StatePublished - Jun 2011
Externally publishedYes


  • Depth
  • Functional data
  • Growth data
  • Precipitation data
  • Space-time data
  • Visualization

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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