The Wrapped Cauchy Distribution

Density, probability distribution function, quantiles, and random generation for the circular wrapped Cauchy distribution with mean \(\mu\) and rho \(\rho\)

Usage

rwcauchy(n, mean, rho)

dwcauchy(theta, mean, rho, axial = FALSE, log = FALSE)

pwcauchy(
  theta,
  mean,
  rho,
  axial = FALSE,
  from = NULL,
  lower.tail = TRUE,
  log.p = FALSE
)

qwcauchy(
  p,
  mean,
  rho,
  axial = FALSE,
  from = NULL,
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

n

integer. Number of observations in degrees

mean

numeric. The mean vector in degrees.

rho

numeric. Concentration parameter in the range (0, 1)

theta

numeric. Angular value in degrees

axial

logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE).

log

logical. If TRUE, probabilities p are given as \(\log(p)\).

from

if NULL is set to \(\mu-\pi\). This is the value from which the pvm and qvm are evaluated. in degrees.

lower.tail

logical. If TRUE (default), probabilities are \(P(\Theta \le \theta)\), otherwise \(P(\Theta > \theta)\).

log.p

logical. If TRUE, probabilities p are given as log(p).

p

numeric. Vector of probabilities with values in \([0,1]\).

Value

dwcauchy gives the density, pwcauchy gives the probability of the wrapped Cauchy distribution function, rwcauchy generates random deviates (in degrees), and qrwcauchy provides quantiles (in degrees).

See also

vonmises and cunif

Examples

set.seed(1)
x <- rwcauchy(5, mean = 90, rho = exp(-1))

dwcauchy(x, mean = 90, rho = exp(-1))
#> [1] 0.002990156 0.001451825 0.001673540 0.005563540 0.004075399
dwcauchy(x, mean = 90, rho = exp(-1), axial = TRUE)
#> [1] 0.003057101 0.004218155 0.002953053 0.009144468 0.004528445

pwcauchy(x, mean = 90, rho = exp(-1))
#> [1] 0.7948404 0.9396023 0.9072813 0.4004565 0.7210158
qwcauchy(c(.25, .5, .75), mean = 90, rho = exp(-1))
#> [1]  40.39506  90.00000 139.60494