dist-snorm: Skew normal distribution

In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

Skew normal distribution

Description

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

Skewness is introduced based on the scheme by Fernandez and Steel (2000). Further, the distribution is standardized as discussed by Wuertz et al (????). Non-zero mean and/or standard deviation different from one can be specified with parameters mean and sd.

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).

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

The skew normal distribution

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

Value

numeric vector

Author(s)

Diethelm Wuertz for the Rmetrics R-port

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

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)

fGarch documentation built on July 12, 2024, 3:01 p.m.