Skew-Normal Distribution

Usage

dsn(x, location, scale, shape)
psn(q, location, scale, shape)
qsn(p, location, scale, shape, tol)
rsn(n, location, scale, shape)

Arguments

x vector of quantiles. Missing values (NaNs) are allowed.
q vector of quantiles. Missing values (NaNs) are allowed.
p vector of probabilities. Missing values (NaNs) are allowed.
location vector of location parameters (default is 0).
scale vector of (positive) scale parameters (default is 1).
shape vector of shape parameters (default is 0). With psn and `qsn", it must be of length 1.
n sample size (default is 1).
tol a scale value which regulates the accuracy of the result (default is 1e-8).

Description

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

Details

psn make use of function T_Owen

Value

density (dsn), probability (psn), quantile (qsn) or random sample (rsn) from the skew-normal distribution with given location, scale and shape parameters.

BACKGROUND

The family of skew-normal distributions is an extension of the normal family, via the introdution of a shape parameter which regulates skewness; when shape=0, the skew-normal distribution reduces to the normal one. The density of the SN distribution when location=0 and scale=1 is 2*dnorm(x)*pnorm(shape*x). A multivariate version of the distribution exists. See the references below for additional information.

References

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715-726.

See Also

T_Owen, dmsn, sn_mle

Examples

pdf = dsn([-3:0.1:3],0,1,3)
cdf = psn([-3:0.1:3],0,1,3)
qu = qsn([0.1:0.1:0.9],0,1,-2)
rn = rsn(100, 5, 2, 5)


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