CircNNTSR: An R Package for the Statistical Analysis of Circular, Multivariate Circular, and Spherical Data Using Nonnegative Trigonometric Sums

• Main Authors: Juan José Fernández-Durán, María Mercedes Gregorio-Domínguez
• Format: Article
• Language: English
• Published: Foundation for Open Access Statistics 2016-05-01
• Series: Journal of Statistical Software
• Subjects: Fourier series; likelihood ratio test; maximum likelihood estimation; smooth Riemann manifold
• Online Access: https://www.jstatsoft.org/index.php/jss/article/view/2689

The statistical analysis of circular, multivariate circular, and spherical data is very important in different areas, such as paleomagnetism, astronomy and biology. The use of nonnegative trigonometric sums allows for the construction of flexible probability models for these types of data to model datasets with skewness and multiple modes. The R package CircNNTSR includes functions to plot, fit by maximum likelihood, and simulate models based on nonnegative trigonometric sums for circular, multivariate circular, and spherical data. For maximum likelihood estimation of the models for the three different types of data an efficient Newton-like algorithm on a hypersphere is used. Examples of applications of the functions provided in the CircNNTSR package to actual and simulated datasets are presented and it is shown how the package can be used to test for uniformity, homogeneity, and independence using likelihood ratio tests.