The box-and-whiskers plot is a very useful exploratory tool that quickly summarizes some of the most important information about an observed distribution. In spite of its many extensions, a proper boxplot for circular data is not yet available. Indeed, such a visualization would be especially useful in environmetrics thanks to its simplicity and strong visual impact: circular measures arise as wind directions, movements of animals from points of release, orientation of fracture planes, just to cite a few. However, while on the line the structure of the box is uniquely defined once the observations are sorted in non-decreasing order, in the circular space this is not allowed given the lack of a natural ordering. Beyond an attempt presenting significant drawbacks, boxplots that take into account the periodic features of circular data are not available in the literature. For this reason, we introduce circular boxplots exploiting some data depth concepts, in analogy with the bagplot for bivariate data. A rule of thumb useful to draw the whiskers is obtained by means of a simulation study. In addition, a discussion on the choice of the depth function is offered. An application to real environmental data is finally provided along with a proposal of a visual display of ‘parallel’ circular boxplots.
EXPLORING ENVIRONMENTAL DATA THROUGH CIRCULAR BOXPLOTS
BUTTARAZZI, Davide;PORZIO, Giovanni Camillo
2015-01-01
Abstract
The box-and-whiskers plot is a very useful exploratory tool that quickly summarizes some of the most important information about an observed distribution. In spite of its many extensions, a proper boxplot for circular data is not yet available. Indeed, such a visualization would be especially useful in environmetrics thanks to its simplicity and strong visual impact: circular measures arise as wind directions, movements of animals from points of release, orientation of fracture planes, just to cite a few. However, while on the line the structure of the box is uniquely defined once the observations are sorted in non-decreasing order, in the circular space this is not allowed given the lack of a natural ordering. Beyond an attempt presenting significant drawbacks, boxplots that take into account the periodic features of circular data are not available in the literature. For this reason, we introduce circular boxplots exploiting some data depth concepts, in analogy with the bagplot for bivariate data. A rule of thumb useful to draw the whiskers is obtained by means of a simulation study. In addition, a discussion on the choice of the depth function is offered. An application to real environmental data is finally provided along with a proposal of a visual display of ‘parallel’ circular boxplots.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
