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.

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.

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

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 May 29, 2024, 8:30 a.m.