Skew-Cauchy Distribution
Density function, distribution function, quantiles and random number generation for the skew-Cauchy (SC) distribution.
dsc(x, xi = 0, omega = 1, alpha = 0, dp = NULL, log = FALSE) psc(x, xi = 0, omega = 1, alpha = 0, dp = NULL) qsc(p, xi = 0, omega = 1, alpha = 0, dp = NULL) rsc(n = 1, xi = 0, omega = 1, alpha = 0, dp = NULL)
x |
vector of quantiles. Missing values ( |
p |
vector of probabilities. Missing values ( |
xi |
vector of location parameters. |
omega |
vector of (positive) scale parameters. |
alpha |
vector of slant parameters. |
dp |
a vector of length 3 whose elements represent the parameters
described above. If |
n |
sample size. |
log |
logical flag used in |
density (dsc), probability (psc), quantile (qsc)
or random sample (rsc) from the skew-Cauchy distribution with given
xi, omega and alpha parameters or from the extended
skew-normal if tau!=0
Typical usages are
dsc(x, xi=0, omega=1, alpha=0, log=FALSE) dsc(x, dp=, log=FALSE) psc(x, xi=0, omega=1, alpha=0) psc(x, dp= ) qsc(p, xi=0, omega=1, alpha=0) qsc(x, dp=) rsc(n=1, xi=0, omega=1, alpha=0) rsc(x, dp=)
The skew-Cauchy distribution can be thought as a skew-t with tail-weight
parameter nu=1. In this case, closed-form expressions of the
distribution function and the quantile function have been obtained by
Behboodian et al. (2006).
The key facts are summarized in Complement 4.2 of Azzalini and Capitanio (2014).
A multivariate version of the distribution exists.
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-normal and Related Families. Cambridge University Press, IMS Monographs series.
Behboodian, J., Jamalizadeh, A., and Balakrishnan, N. (2006). A new class of skew-Cauchy distributions. Statist. Probab. Lett. 76, 1488–1493.
pdf <- dsc(seq(-5,5,by=0.1), alpha=3) cdf <- psc(seq(-5,5,by=0.1), alpha=3) q <- qsc(seq(0.1,0.9,by=0.1), alpha=-2) p <- psc(q, alpha=-2) rn <- rsc(100, 5, 2, 5)
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