sph_stat_distr: Asymptotic distributions for spherical uniformity statistics

In sphunif: Uniformity Tests on the Circle, Sphere, and Hypersphere

Asymptotic distributions for spherical uniformity statistics

Description

Computation of the asymptotic null distributions of spherical uniformity statistics.

Usage

p_sph_stat_Bingham(x, p)

d_sph_stat_Bingham(x, p)

p_sph_stat_CJ12(x, regime = 1L, beta = 0)

d_sph_stat_CJ12(x, regime = 3L, beta = 0)

p_sph_stat_Rayleigh(x, p)

d_sph_stat_Rayleigh(x, p)

p_sph_stat_Rayleigh_HD(x, p)

d_sph_stat_Rayleigh_HD(x, p)

p_sph_stat_Ajne(x, p, K_max = 1000, thre = 0, ...)

d_sph_stat_Ajne(x, p, K_max = 1000, thre = 0, ...)

p_sph_stat_Bakshaev(x, p, K_max = 1000, thre = 0, ...)

d_sph_stat_Bakshaev(x, p, K_max = 1000, thre = 0, ...)

p_sph_stat_Gine_Fn(x, p, K_max = 1000, thre = 0, ...)

d_sph_stat_Gine_Fn(x, p, K_max = 1000, thre = 0, ...)

p_sph_stat_Gine_Gn(x, p, K_max = 1000, thre = 0, ...)

d_sph_stat_Gine_Gn(x, p, K_max = 1000, thre = 0, ...)

p_sph_stat_PAD(x, p, K_max = 1000, thre = 0, ...)

d_sph_stat_PAD(x, p, K_max = 1000, thre = 0, ...)

p_sph_stat_PCvM(x, p, K_max = 1000, thre = 0, ...)

d_sph_stat_PCvM(x, p, K_max = 1000, thre = 0, ...)

p_sph_stat_PRt(x, p, t = 1/3, K_max = 1000, thre = 0, ...)

d_sph_stat_PRt(x, p, t = 1/3, K_max = 1000, thre = 0, ...)

p_sph_stat_Riesz(x, p, s = 1, K_max = 1000, thre = 0, ...)

d_sph_stat_Riesz(x, p, s = 1, K_max = 1000, thre = 0, ...)

Arguments

x	a vector of size nx or a matrix of size c(nx, 1).
p	integer giving the dimension of the ambient space R^p that contains S^{p-1}.
regime	type of asymptotic regime for the CJ12 test, either 1 (sub-exponential regime), 2 (exponential), or 3 (super-exponential; default).
beta	\beta parameter in the exponential regime of the CJ12 test, a nonnegative real. Defaults to 0.
K_max	integer giving the truncation of the series that compute the asymptotic p-value of a Sobolev test. Defaults to 1e3.
thre	error threshold for the tail probability given by the the first terms of the truncated series of a Sobolev test. Defaults to 0 (no further truncation).
...	further parameters passed to p_Sobolev or d_Sobolev (such as x_tail).
t	t parameter for the Rothman and Cressie tests, a real in (0, 1). Defaults to 1 / 3.
s	s parameter for the s-Riesz test, a real in (0, 2). Defaults to 1.

Details

Descriptions and references on most of the asymptotic distributions are available in García-Portugués and Verdebout (2018).

Value

• r_sph_stat_*: a matrix of size c(n, 1) containing the sample.

• p_sph_stat_*, d_sph_stat_*: a matrix of size c(nx, 1) with the evaluation of the distribution or density functions at x.

Examples

# Ajne
curve(d_sph_stat_Ajne(x, p = 3, method = "HBE"), n = 2e2, ylim = c(0, 4))
curve(p_sph_stat_Ajne(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

# Bakshaev
curve(d_sph_stat_Bakshaev(x, p = 3, method = "HBE"), to = 5, n = 2e2,
      ylim = c(0, 2))
curve(p_sph_stat_Bakshaev(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

# Bingham
curve(d_sph_stat_Bingham(x, p = 3), to = 20, n = 2e2, ylim = c(0, 1))
curve(p_sph_stat_Bingham(x, p = 3), n = 2e2, col = 2, add = TRUE)

# CJ12
curve(d_sph_stat_CJ12(x, regime = 1), from = -10, to = 10, n = 2e2,
      ylim = c(0, 1))
curve(d_sph_stat_CJ12(x, regime = 2, beta = 0.1), n = 2e2, col = 2,
      add = TRUE)
curve(d_sph_stat_CJ12(x, regime = 3), n = 2e2, col = 3, add = TRUE)
curve(p_sph_stat_CJ12(x, regime = 1), n = 2e2, col = 1, add = TRUE)
curve(p_sph_stat_CJ12(x, regime = 2, beta = 0.1), n = 2e2, col = 2,
      add = TRUE)
curve(p_sph_stat_CJ12(x, regime = 3), col = 3, add = TRUE)

# Gine Fn
curve(d_sph_stat_Gine_Fn(x, p = 3, method = "HBE"), to = 2, n = 2e2,
      ylim = c(0, 2))
curve(p_sph_stat_Gine_Fn(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

# Gine Gn
curve(d_sph_stat_Gine_Gn(x, p = 3, method = "HBE"), to = 1.5, n = 2e2,
      ylim = c(0, 2.5))
curve(p_sph_stat_Gine_Gn(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

# PAD
curve(d_sph_stat_PAD(x, p = 3, method = "HBE"), to = 3, n = 2e2,
      ylim = c(0, 1.5))
curve(p_sph_stat_PAD(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

# PCvM
curve(d_sph_stat_PCvM(x, p = 3, method = "HBE"), to = 0.6, n = 2e2,
      ylim = c(0, 7))
curve(p_sph_stat_PCvM(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

# PRt
curve(d_sph_stat_PRt(x, p = 3, method = "HBE"), n = 2e2, ylim = c(0, 5))
curve(p_sph_stat_PRt(x, p = 3, method = "HBE"), n = 2e2, col = 2, add = TRUE)

# Rayleigh
curve(d_sph_stat_Rayleigh(x, p = 3), to = 15, n = 2e2, ylim = c(0, 1))
curve(p_sph_stat_Rayleigh(x, p = 3), n = 2e2, col = 2, add = TRUE)

# HD-standardized Rayleigh
curve(d_sph_stat_Rayleigh_HD(x, p = 3), from = -4, to = 4, n = 2e2,
      ylim = c(0, 1))
curve(p_sph_stat_Rayleigh_HD(x, p = 3), n = 2e2, col = 2, add = TRUE)

# Riesz
curve(d_sph_stat_Riesz(x, p = 3, method = "HBE"), n = 2e2, from = 0, to = 5,
      ylim = c(0, 2))
curve(p_sph_stat_Riesz(x, p = 3, method = "HBE"), n = 2e2, col = 2,
      add = TRUE)

sphunif documentation built on Aug. 21, 2023, 9:11 a.m.