sn (version 2.1.1)

dsc: Skew-Cauchy Distribution

Description

Density function, distribution function, quantiles and random number generation for the skew-Cauchy (SC) distribution.

Usage

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)

Value

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

Arguments

x

vector of quantiles. Missing values (NAs) and Inf's are allowed.

p

vector of probabilities. Missing values (NAs) are allowed.

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 dp is specified, the individual parameters cannot be set.

n

sample size.

log

logical flag used in dsc (default FALSE). When TRUE, the logarithm of the density values is returned.

Background

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.

Details

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=)

References

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.

See Also

dst, dmsc

Examples

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)