biv_lrt {ridgetorus} | R Documentation |
Performs the following likelihood ratio tests for the
concentrations in bivariate sine von Mises and wrapped Cauchy distributions:
(1) homogeneity: H_0:\kappa_1=\kappa_2
vs.
H_1:\kappa_1\neq\kappa_2
, and H_0:\xi_1=\xi_2
vs.
H_1:\xi_1\neq\xi_2
, respectively;
(2) independence: H_0:\lambda=0
vs.
H_1:\lambda\neq0
, and H_0:\rho=0
vs. H_1:\rho\neq0
.
The tests (1) and (2) can be performed simultaneously.
biv_lrt(x, hom = FALSE, indep = FALSE, fit_mle = NULL, type, ...)
x |
matrix of dimension |
hom |
test the homogeneity hypothesis? Defaults to |
indep |
test the independence hypothesis? Defaults to |
fit_mle |
output of |
type |
either |
... |
optional parameters passed to |
A list with class htest
:
statistic |
the value of the likelihood ratio test statistic. |
p.value |
the |
alternative |
a character string describing the alternative hypothesis. |
method |
description of the type of test performed. |
df |
degrees of freedom. |
data.name |
a character string giving the name of |
fit_mle |
maximum likelihood fit. |
fit_null |
maximum likelihood fit under the null hypothesis. |
Kato, S. and Pewsey, A. (2015). A Möbius transformation-induced distribution on the torus. Biometrika, 102(2):359–370. doi:10.1093/biomet/asv003
Singh, H., Hnizdo, V., and Demchuk, E. (2002). Probabilistic model for two dependent circular variables. Biometrika, 89(3):719–723. doi:10.1093/biomet/89.3.719
## Bivariate sine von Mises
# Homogeneity
n <- 200
mu <- c(0, 0)
kappa_0 <- c(1, 1, 0.5)
kappa_1 <- c(0.7, 0.1, 0.25)
samp_0 <- r_bvm(n = n, mu = mu, kappa = kappa_0)
samp_1 <- r_bvm(n = n, mu = mu, kappa = kappa_1)
biv_lrt(x = samp_0, hom = TRUE, type = "bvm")
biv_lrt(x = samp_1, hom = TRUE, type = "bvm")
# Independence
kappa_0 <- c(0, 1, 0)
kappa_1 <- c(1, 0, 1)
samp_0 <- r_bvm(n = n, mu = mu, kappa = kappa_0)
samp_1 <- r_bvm(n = n, mu = mu, kappa = kappa_1)
biv_lrt(x = samp_0, indep = TRUE, type = "bvm")
biv_lrt(x = samp_1, indep = TRUE, type = "bvm")
# Independence and homogeneity
kappa_0 <- c(3, 3, 0)
kappa_1 <- c(3, 1, 0)
samp_0 <- r_bvm(n = n, mu = mu, kappa = kappa_0)
samp_1 <- r_bvm(n = n, mu = mu, kappa = kappa_1)
biv_lrt(x = samp_0, indep = TRUE, hom = TRUE, type = "bvm")
biv_lrt(x = samp_1, indep = TRUE, hom = TRUE, type = "bvm")
## Bivariate wrapped Cauchy
# Homogeneity
xi_0 <- c(0.5, 0.5, 0.25)
xi_1 <- c(0.7, 0.1, 0.5)
samp_0 <- r_bwc(n = n, mu = mu, xi = xi_0)
samp_1 <- r_bwc(n = n, mu = mu, xi = xi_1)
biv_lrt(x = samp_0, hom = TRUE, type = "bwc")
biv_lrt(x = samp_1, hom = TRUE, type = "bwc")
# Independence
xi_0 <- c(0.1, 0.5, 0)
xi_1 <- c(0.3, 0.5, 0.2)
samp_0 <- r_bwc(n = n, mu = mu, xi = xi_0)
samp_1 <- r_bwc(n = n, mu = mu, xi = xi_1)
biv_lrt(x = samp_0, indep = TRUE, type = "bwc")
biv_lrt(x = samp_1, indep = TRUE, type = "bwc")
# Independence and homogeneity
xi_0 <- c(0.2, 0.2, 0)
xi_1 <- c(0.1, 0.2, 0.1)
samp_0 <- r_bwc(n = n, mu = mu, xi = xi_0)
samp_1 <- r_bwc(n = n, mu = mu, xi = xi_1)
biv_lrt(x = samp_0, indep = TRUE, hom = TRUE, type = "bwc")
biv_lrt(x = samp_1, indep = TRUE, hom = TRUE, type = "bwc")