# fboxplot: Functional bagplot and functional HDR boxplot In rainbow: Bagplots, Boxplots and Rainbow Plots for Functional Data

## Description

Compute bivariate bagplot, functional bagplot and bivariate HDR boxplot, functional HDR boxplot.

## Usage

 1 2 3 4 5 fboxplot(data, plot.type = c("functional", "bivariate"), type = c("bag", "hdr"), alpha = c(0.05, 0.5), projmethod = c("PCAproj","rapca"), factor = 1.96, na.rm = TRUE, xlab = data\$xname, ylab = data\$yname, shadecols = gray((9:1)/10), pointcol = 1, plotlegend = TRUE, legendpos = "topright", ncol = 2, ...)

## Arguments

 data An object of class fds or fts. plot.type Version of boxplot. When plot.type="functional", a functional plot is provided. When plot.type="bivariate", a square bivariate plot is provided. type Type of boxplot. When type = "bag", a bagplot is provided. When type = "hdr", a HDR boxplot is provided. alpha Coverage probability for the functional HDR boxplot. alpha are the coverage percentages of the outliers and the central region. factor When type = "bag", the outer region of a bagplot is the convex hull obtained by inflating the inner region by the bagplot factor. na.rm Remove missing values. xlab A title for the x axis. ylab A title for the y axis. shadecols Colors for shaded regions. pointcol Color for outliers and mode. plotlegend Add a legend to the graph. legendpos Legend position. By default, it is the top right corner. ncol Number of columns in the legend. projmethod Method used for projection. ... Other arguments.

## Details

The functional curves are first projected into a finite dimensional subspace via functional principal component decomposition. For simiplicity, we choose the subspace as R^2. Based on Tukey (1974)'s halfspace bagplot and Hyndman (1996)'s HDR boxplot, we order each data point in R^2 by data depth and data density. Outliers are those that have either lowest depth (distance from the centre) or lowest density.

## Value

Function produces a graphical plot.

## Author(s)

Rob J Hyndman, Han Lin Shang. Please, report bugs and suggestions to hanlin.shang@anu.edu.au

## References

J. W. Tukey (1974) "Mathematics and the picturing of data", Proceedings of the International Congress of Mathematicians, 2, 523-532, Canadian Mathematical Congress, Montreal.

P. Rousseeuw, I. Ruts and J. Tukey (1999) "The bagplot: A bivariate boxplot", The American Statistician, 53(4), 382-387.

R. J. Hyndman (1996) "Computing and graphing highest density regions", The American Statistician, 50(2), 120-126.

R. J. Hyndman and H. L. Shang (2010) "Rainbow plots, bagplots, and boxplots for functional data", Journal of Computational and Graphical Statistics, 19(1), 29-45.

Y. Sun and M. G. Genton (2011) "Functional boxplots", Journal of Computational and Graphical Statistics, 20(2), 316-334.

Y. Sun and M. G. Genton (2012) "Adjusted functional boxplots for spatio-temporal data visualization and outlier detection", Environmetrics, 23, 54-64.

Y. Sun and M. G. Genton (2012) "Functional median polish", Journal of Agricultural, Biological, and Environmental Statistics, 17, 354-376.

## Examples

 1 2 3 4 fboxplot(data = ElNino_OISST_region_1and2, plot.type = "functional", type = "bag", projmethod="PCAproj") fboxplot(data = ElNino_OISST_region_1and2, plot.type = "bivariate", type = "bag", projmethod="PCAproj")