dsn {sn} | R Documentation |
Density function, distribution function, quantiles and random number generation for the skew-normal (SN) and the extended skew-normal (ESN) distribution.
dsn(x, xi=0, omega=1, alpha=0, tau=0, dp=NULL, log=FALSE) psn(x, xi=0, omega=1, alpha=0, tau=0, dp=NULL, engine, ...) qsn(p, xi=0, omega=1, alpha=0, tau=0, dp=NULL, tol=1e-8, ...) rsn(n=1, xi=0, omega=1, alpha=0, tau=0, dp=NULL)
x |
vector of quantiles. Missing values ( |
p |
vector of probabilities. Missing values ( |
xi |
vector of location parameters. |
omega |
vector of scale parameters; must be positive. |
alpha |
vector of slant parameters; |
tau |
a single value representing the ‘hidden mean’ parameter
of the ESN distribution; |
dp |
a vector of length 3 (in the SN case) or
4 (in the ESN case), whose components represent
the individual parameters described above. If |
n |
sample size. |
tol |
a scalar value which regulates the accuracy of the result of
|
log |
logical flag used in |
engine |
a character string which selects the computing engine;
this is either |
... |
additional parameters passed to |
density (dsn
), probability (psn
), quantile (qsn
)
or random sample (rsn
) from the skew-normal distribution with given
xi
, omega
and alpha
parameters or from the extended
skew-normal if tau!=0
Typical usages are
dsn(x, xi=0, omega=1, alpha=0, log=FALSE) dsn(x, dp=, log=FALSE) psn(x, xi=0, omega=1, alpha=0, ...) psn(x, dp=, ...) qsn(p, xi=0, omega=1, alpha=0, tol=1e-8, ...) qsn(x, dp=, ...) rsn(n=1, xi=0, omega=1, alpha=0) rsn(x, dp=)
psn
and qsn
make use of function T.Owen
or biv.nt.prob
The family of skew-normal distributions is an extension of the normal
family, via the introdution of a alpha
parameter which regulates
asymmetry; when alpha=0
, the skew-normal distribution reduces to
the normal one. The density function of the SN distribution
in the ‘normalized’ case having xi=0
and omega=1
is
2*dnorm(x)*pnorm(alpha*x)
.
An early discussion of the skew-normal distribution is given by
Azzalini (1985); see Section 3.3 for the ESN variant,
up to a slight difference in the parameterization.
An updated extensive account is provided by Chapter 2 of Azzalini and
Capitanio (2014); the ESN variant is presented Section 2.2.
A multivariate version of the distribution is examined in Chapter 5.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
Functions used by psn
:
T.Owen
, biv.nt.prob
Related distributions: dmsn
, dst
,
dmst
pdf <- dsn(seq(-3, 3, by=0.1), alpha=3) cdf <- psn(seq(-3, 3, by=0.1), alpha=3) q <- qsn(seq(0.1, 0.9, by=0.1), alpha=-2) r <- rsn(100, 5, 2, 5)