# Skew normal distribution

`dist-snorm.Rd`

Functions to compute density, distribution function, quantile function and to generate random variates for the skew normal distribution.

The distribution is standardized as discussed in the reference by Wuertz et al below.

## 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.

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

## Details

`dsnorm`

computed the density,
`psnorm`

the distribution function,
`qsnorm`

the quantile function,
and
`rsnorm`

generates random deviates.

## 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

## See also

`snormFit`

(fit),
`snormSlider`

(visualize),

## 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
```