This book gives a collection of statistical methods suitable for the analysis of spherical data. The emphasis of the book is on providing practical advice for applied workers, and many mathematical details are only briefly sketched or omitted. A more mathematical, though less comprehensive study of methods for spherical data can be found in the classic monograph by K. V. Mardia, Statistics of directional data (1972; Zbl 0244.62005).
There is also much valuable common-sense statistical advice based on recent developments on graphical methods, outliers, nonparametric analysis, model assessment and exploratory analysis. Topics discussed for directional data (unit vectors on the sphere) include the Fisher distribution, the spherical mean and median, unimodality, rotational symmetry, small circle distributions and multimodality. Topics for axial data (in which antipodal directions are identified) include the Watson distribution, bipolar and girdle behaviour, and multimodality. Methods are also given for the analysis of two or more samples.
Reviewers note: Some of the correlations proposed for spherical data are incorrect. In the Jupp-Mardia correlation for directional data defined on p. 238, the covariance matrices need to be centered about the means of X and Y, respectively. Further the definition of the Jupp-Mardia correlation for axial data on p. 235 is inappropriate; a more complicated construction is needed.