Uniformity Tests on the Circle, Sphere, and Hypersphere
Weighted sums of non-central chi squared random variables
Sample uniformly distributed circular and spherical data
Surface area of the intersection of two hyperspherical caps
Conversion between angular and Cartesian coordinates of the (hyper)sph...
Available circular and (hyper)spherical uniformity tests
The incomplete beta function and its inverse
Density and distribution of a chi squared
Transforming between polar and Cartesian coordinates
Circular gaps
Statistics for testing circular uniformity
Asymptotic distributions for circular uniformity statistics
Efficient evaluation of the empirical cumulative distribution function
Distribution and quantile functions from angular function
Gauss--Legendre quadrature
Gegenbauer polynomials and coefficients
Asymptotic distributions of Sobolev statistics of spherical uniformity
(Hyper)spherical harmonics
Monte Carlo integration of functions on the (hyper)sphere
Local projected alternatives to uniformity
Utilities for projected-ecdf statistics of spherical uniformity
Projection of the spherical uniform distribution
Shortest angles matrix
Sample non-uniformly distributed spherical data
Circular and (hyper)spherical uniformity tests
Transformation between different coefficients in Sobolev statistics
Sort the columns of a matrix
Statistics for testing (hyper)spherical uniformity
Asymptotic distributions for spherical uniformity statistics
Finite Sobolev statistics for testing (hyper)spherical uniformity
sphunif: Uniformity Tests on the Circle, Sphere, and Hypersphere
Uniform spherical cap distribution
Circular and (hyper)spherical uniformity statistics
Null distributions for circular and (hyper)spherical uniformity statis...
Monte Carlo simulation of circular and (hyper)spherical uniformity sta...
Low-level utilities for sphunif
Utilities for weighted sums of non-central chi squared random variable...
Implementation of uniformity tests on the circle and (hyper)sphere. The main function of the package is unif_test(), which conveniently collects more than 35 tests for assessing uniformity on S^{p-1} = {x in R^p : ||x|| = 1}, p >= 2. The test statistics are implemented in the unif_stat() function, which allows computing several statistics for different samples within a single call, thus facilitating Monte Carlo experiments. Furthermore, the unif_stat_MC() function allows parallelizing them in a simple way. The asymptotic null distributions of the statistics are available through the function unif_stat_distr(). The core of 'sphunif' is coded in C++ by relying on the 'Rcpp' package. The package also provides several novel datasets and gives the replicability for the data applications/simulations in García-Portugués et al. (2021) <doi:10.1007/978-3-030-69944-4_12>, García-Portugués et al. (2023) <doi:10.3150/21-BEJ1454>, García-Portugués et al. (2024) <doi:10.48550/arXiv.2108.09874>, and Fernández-de-Marcos and García-Portugués (2024) <doi:10.48550/arXiv.2405.13531>.