# Uniformity Tests on the Circle, Sphere, and Hypersphere

## Documentation for package ‘sphunif’ version 1.4.0

- DESCRIPTION file.
- Package NEWS.

## Help Pages

A B C D F G H I L P Q R S T U V W X

sphunif-package | 'sphunif': Uniformity Tests on the Circle, Sphere, and Hypersphere

## -- A --

akx | Utilities for projected-ecdf statistics of spherical uniformity
angles_to_sphere | Conversion between angular and Cartesian coordinates of the (hyper)sphere
avail_cir_tests | Available circular and (hyper)spherical uniformity tests
avail_sph_tests | Available circular and (hyper)spherical uniformity tests
avail_tests | Available circular and (hyper)spherical uniformity tests
A_theta_x | Surface area of the intersection of two hyperspherical caps

## -- B --

bk_to_uk | Transformation between different coefficients in Sobolev statistics
bk_to_vk2 | Transformation between different coefficients in Sobolev statistics

## -- C --

cir_coord_conv | Transforming between polar and Cartesian coordinates
cir_gaps | Circular gaps
cir_stat | Statistics for testing circular uniformity
cir_stat_Ajne | Statistics for testing circular uniformity
cir_stat_Bakshaev | Statistics for testing circular uniformity
cir_stat_Bingham | Statistics for testing circular uniformity
cir_stat_CCF09 | Statistics for testing circular uniformity
cir_stat_Cressie | Statistics for testing circular uniformity
cir_stat_distr | Asymptotic distributions for circular uniformity statistics
cir_stat_FG01 | Statistics for testing circular uniformity
cir_stat_Gine_Fn | Statistics for testing circular uniformity
cir_stat_Gine_Gn | Statistics for testing circular uniformity
cir_stat_Gini | Statistics for testing circular uniformity
cir_stat_Gini_squared | Statistics for testing circular uniformity
cir_stat_Greenwood | Statistics for testing circular uniformity
cir_stat_Hermans_Rasson | Statistics for testing circular uniformity
cir_stat_Hodges_Ajne | Statistics for testing circular uniformity
cir_stat_Kuiper | Statistics for testing circular uniformity
cir_stat_Log_gaps | Statistics for testing circular uniformity
cir_stat_Max_uncover | Statistics for testing circular uniformity
cir_stat_Num_uncover | Statistics for testing circular uniformity
cir_stat_PAD | Statistics for testing circular uniformity
cir_stat_PCvM | Statistics for testing circular uniformity
cir_stat_Poisson | Statistics for testing circular uniformity
cir_stat_PRt | Statistics for testing circular uniformity
cir_stat_Pycke | Statistics for testing circular uniformity
cir_stat_Pycke_q | Statistics for testing circular uniformity
cir_stat_Range | Statistics for testing circular uniformity
cir_stat_Rao | Statistics for testing circular uniformity
cir_stat_Rayleigh | Statistics for testing circular uniformity
cir_stat_Riesz | Statistics for testing circular uniformity
cir_stat_Rothman | Statistics for testing circular uniformity
cir_stat_Sobolev | Finite Sobolev statistics for testing (hyper)spherical uniformity
cir_stat_Softmax | Statistics for testing circular uniformity
cir_stat_Vacancy | Statistics for testing circular uniformity
cir_stat_Watson | Statistics for testing circular uniformity
cir_stat_Watson_1976 | Statistics for testing circular uniformity
comets | Comet orbits
con_f | Local projected alternatives to uniformity
craters | Craters named by the IUA
cutoff_locdev | Local projected alternatives to uniformity
cutoff_wschisq | Weighted sums of non-central chi squared random variables
c_unif_cap | Uniform spherical cap distribution

## -- D --

d_cir_stat_Ajne | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Bakshaev | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Bingham | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Gine_Fn | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Gine_Gn | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Gini | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Gini_squared | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Greenwood | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Hermans_Rasson | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Hodges_Ajne | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Kuiper | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Log_gaps | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Max_uncover | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Num_uncover | Asymptotic distributions for circular uniformity statistics
d_cir_stat_PAD | Asymptotic distributions for circular uniformity statistics
d_cir_stat_PCvM | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Poisson | Asymptotic distributions for circular uniformity statistics
d_cir_stat_PRt | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Pycke | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Pycke_q | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Range | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Rao | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Rayleigh | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Riesz | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Rothman | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Sobolev | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Softmax | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Vacancy | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Watson | Asymptotic distributions for circular uniformity statistics
d_cir_stat_Watson_1976 | Asymptotic distributions for circular uniformity statistics
d_Kolmogorov | Asymptotic distributions for circular uniformity statistics
d_locdev | Local projected alternatives to uniformity
d_proj_unif | Projection of the spherical uniform distribution
d_proj_unif_cap | Uniform spherical cap distribution
d_p_k | Asymptotic distributions of Sobolev statistics of spherical uniformity
d_Sobolev | Asymptotic distributions of Sobolev statistics of spherical uniformity
d_sph_stat_Ajne | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Bakshaev | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Bingham | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_CJ12 | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Gine_Fn | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Gine_Gn | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_PAD | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_PCvM | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Poisson | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_PRt | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Rayleigh | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Rayleigh_HD | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Riesz | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Sobolev | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Softmax | Asymptotic distributions for spherical uniformity statistics
d_sph_stat_Stereo | Asymptotic distributions for spherical uniformity statistics
d_unif_cap | Uniform spherical cap distribution
d_wschisq | Weighted sums of non-central chi squared random variables

## -- F --

F_from_f | Distribution and quantile functions from angular function
F_inv_from_f | Distribution and quantile functions from angular function
f_locdev | Local projected alternatives to uniformity
f_locdev_Pn | Utilities for projected-ecdf statistics of spherical uniformity

## -- G --

Gauss_Legen | Gauss-Legendre quadrature
Gauss_Legen_nodes | Gauss-Legendre quadrature
Gauss_Legen_weights | Gauss-Legendre quadrature
Gegenbauer | Gegenbauer polynomials and coefficients
Gegen_coefs | Gegenbauer polynomials and coefficients
Gegen_coefs_2d | Gegenbauer polynomials and coefficients
Gegen_coefs_Pn | Utilities for projected-ecdf statistics of spherical uniformity
Gegen_norm | Gegenbauer polynomials and coefficients
Gegen_norm_2d | Gegenbauer polynomials and coefficients
Gegen_polyn | Gegenbauer polynomials and coefficients
Gegen_polyn_2d | Gegenbauer polynomials and coefficients
Gegen_series | Gegenbauer polynomials and coefficients
Gegen_series_2d | Gegenbauer polynomials and coefficients
g_i_k | (Hyper)spherical harmonics

## -- H --

harmonics | (Hyper)spherical harmonics

## -- I --

int_sph_MC | Monte Carlo integration of functions on the (hyper)sphere

## -- L --

locdev | Local projected alternatives to uniformity

## -- P --

planets | Planet orbits
Pn | Utilities for projected-ecdf statistics of spherical uniformity
proj_unif | Projection of the spherical uniform distribution
Psi | Shortest angles matrix
Psi_mat | Shortest angles matrix
psi_Pn | Utilities for projected-ecdf statistics of spherical uniformity
p_cir_stat_Ajne | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Bakshaev | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Bingham | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Gine_Fn | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Gine_Gn | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Gini | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Gini_squared | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Greenwood | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Hermans_Rasson | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Hodges_Ajne | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Hodges_Ajne2 | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Kuiper | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Log_gaps | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Max_uncover | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Num_uncover | Asymptotic distributions for circular uniformity statistics
p_cir_stat_PAD | Asymptotic distributions for circular uniformity statistics
p_cir_stat_PCvM | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Poisson | Asymptotic distributions for circular uniformity statistics
p_cir_stat_PRt | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Pycke | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Pycke_q | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Range | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Rao | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Rayleigh | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Riesz | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Rothman | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Sobolev | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Softmax | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Vacancy | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Watson | Asymptotic distributions for circular uniformity statistics
p_cir_stat_Watson_1976 | Asymptotic distributions for circular uniformity statistics
p_Kolmogorov | Asymptotic distributions for circular uniformity statistics
p_proj_unif | Projection of the spherical uniform distribution
p_proj_unif_cap | Uniform spherical cap distribution
p_Sobolev | Asymptotic distributions of Sobolev statistics of spherical uniformity
p_sph_stat_Ajne | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Bakshaev | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Bingham | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_CJ12 | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Gine_Fn | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Gine_Gn | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_PAD | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_PCvM | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Poisson | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_PRt | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Rayleigh | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Rayleigh_HD | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Riesz | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Sobolev | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Softmax | Asymptotic distributions for spherical uniformity statistics
p_sph_stat_Stereo | Asymptotic distributions for spherical uniformity statistics
p_wschisq | Weighted sums of non-central chi squared random variables

## -- Q --

q_proj_unif | Projection of the spherical uniform distribution
q_proj_unif_cap | Uniform spherical cap distribution
q_Sobolev | Asymptotic distributions of Sobolev statistics of spherical uniformity
q_wschisq | Weighted sums of non-central chi squared random variables

## -- R --

rhea | Rhea craters from Hirata (2016)
r_alt | Sample non-uniformly distributed spherical data
r_locdev | Local projected alternatives to uniformity
r_proj_unif | Projection of the spherical uniform distribution
r_proj_unif_cap | Uniform spherical cap distribution
r_unif | Sample uniformly distributed circular and spherical data
r_unif_cap | Uniform spherical cap distribution
r_unif_cir | Sample uniformly distributed circular and spherical data
r_unif_sph | Sample uniformly distributed circular and spherical data
r_wschisq | Weighted sums of non-central chi squared random variables

## -- S --

Sobolev | Asymptotic distributions of Sobolev statistics of spherical uniformity
Sobolev_coefs | Transformation between different coefficients in Sobolev statistics
sphere_to_angles | Conversion between angular and Cartesian coordinates of the (hyper)sphere
sphunif | 'sphunif': Uniformity Tests on the Circle, Sphere, and Hypersphere
sph_stat | Statistics for testing (hyper)spherical uniformity
sph_stat_Ajne | Statistics for testing (hyper)spherical uniformity
sph_stat_Bakshaev | Statistics for testing (hyper)spherical uniformity
sph_stat_Bingham | Statistics for testing (hyper)spherical uniformity
sph_stat_CCF09 | Statistics for testing (hyper)spherical uniformity
sph_stat_CJ12 | Statistics for testing (hyper)spherical uniformity
sph_stat_distr | Asymptotic distributions for spherical uniformity statistics
sph_stat_Gine_Fn | Statistics for testing (hyper)spherical uniformity
sph_stat_Gine_Gn | Statistics for testing (hyper)spherical uniformity
sph_stat_PAD | Statistics for testing (hyper)spherical uniformity
sph_stat_PCvM | Statistics for testing (hyper)spherical uniformity
sph_stat_Poisson | Statistics for testing (hyper)spherical uniformity
sph_stat_PRt | Statistics for testing (hyper)spherical uniformity
sph_stat_Pycke | Statistics for testing (hyper)spherical uniformity
sph_stat_Rayleigh | Statistics for testing (hyper)spherical uniformity
sph_stat_Rayleigh_HD | Statistics for testing (hyper)spherical uniformity
sph_stat_Riesz | Statistics for testing (hyper)spherical uniformity
sph_stat_Sobolev | Finite Sobolev statistics for testing (hyper)spherical uniformity
sph_stat_Softmax | Statistics for testing (hyper)spherical uniformity
sph_stat_Stereo | Statistics for testing (hyper)spherical uniformity

## -- T --

Theta_to_X | Transforming between polar and Cartesian coordinates

## -- U --

uk_to_bk | Transformation between different coefficients in Sobolev statistics
uk_to_vk2 | Transformation between different coefficients in Sobolev statistics
unif_cap | Uniform spherical cap distribution
unif_stat | Circular and (hyper)spherical uniformity statistics
unif_stat_distr | Null distributions for circular and (hyper)spherical uniformity statistics
unif_stat_MC | Monte Carlo simulation of circular and (hyper)spherical uniformity statistics
unif_test | Circular and (hyper)spherical uniformity tests
upper_tri_ind | Shortest angles matrix

## -- V --

venus | Venus craters
vk2_to_bk | Transformation between different coefficients in Sobolev statistics
vk2_to_uk | Transformation between different coefficients in Sobolev statistics

## -- W --

weights_dfs_Sobolev | Asymptotic distributions of Sobolev statistics of spherical uniformity
wschisq | Weighted sums of non-central chi squared random variables

## -- X --

X_to_Theta | Transforming between polar and Cartesian coordinates