Skew normal distribution

Functions to compute density, distribution function, quantile function and to generate random variates for the skew normal distribution. Note that there are different ways to define a skew normal distribution, check section Details to see if this is the distribution you want.

Usage

dsnorm(x, mean = 0, sd = 1, xi = 1.5, log = FALSE)
psnorm(q, mean = 0, sd = 1, xi = 1.5)
qsnorm(p, mean = 0, sd = 1, xi = 1.5)
rsnorm(n, mean = 0, sd = 1, xi = 1.5)

Arguments

x, q

a numeric vector of quantiles.

p

a numeric vector of probabilities.

n

the number of observations.

mean

location parameter.

sd

scale parameter.

xi

skewness parameter, a positive number. xi = 1 gives a symmetric distribution (here normal).

log

a logical; if TRUE, densities are given as log densities.

Details

Skewness is based on the scheme by Fernandez and Steel (2000) but with different parameterisation as discussed by Wuertz et al (????), in that the skewness (xi), mean (mean) and standard deviation (sd) are independent parameters.

Please note that there are different ways to define a 'skew normal distribution'. In particular, the distribution discussed here is different from what is usually referred to as 'skew normal distribution' (see, for example, Azzalini 1985).

dsnorm computes the density, psnorm the distribution function, qsnorm the quantile function, and rsnorm generates random deviates.

Value

numeric vector

References

Fernandez C., Steel M.F.J. (2000); On Bayesian Modelling of Fat Tails and Skewness, Preprint, 31 pages.

Wuertz D., Chalabi Y. and Luksan L. (????); Parameter estimation of ARMA models with GARCH/APARCH errors: An R and SPlus software implementation, Preprint, 41 pages, https://github.com/GeoBosh/fGarchDoc/blob/master/WurtzEtAlGarch.pdf

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

Author

Diethelm Wuertz for the Rmetrics R-port

See also

snormFit (fit), snormSlider (visualize),

sstd (skew Student-t), sged (skew GED)

Examples

## snorm -
   # Ranbdom Numbers:
   par(mfrow = c(2, 2))
   set.seed(1953)
   r = rsnorm(n = 1000)
   plot(r, type = "l", main = "snorm", col = "steelblue")
   
   # Plot empirical density and compare with true density:
   hist(r, n = 25, probability = TRUE, border = "white", col = "steelblue")
   box()
   x = seq(min(r), max(r), length = 201)
   lines(x, dsnorm(x), lwd = 2)
   
   # Plot df and compare with true df:
   plot(sort(r), (1:1000/1000), main = "Probability", col = "steelblue",
     ylab = "Probability")
   lines(x, psnorm(x), lwd = 2)
   
   # Compute quantiles:
   round(qsnorm(psnorm(q = seq(-1, 5, by = 1))), digits = 6)
#> [1] -1  0  1  2  3  4  5