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 (`NaN`s) are allowed.
`q`	vector of quantiles. Missing values (`NaN`s) are allowed.
`p`	vector of probabilities. Missing values (`NaN`s) 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.

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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