Skew normal distribution
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.
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)
- x, q
a numeric vector of quantiles.
a numeric vector of probabilities.
the number of observations.
a logical; if TRUE, densities are given as log densities.
dsnorm computed the density,
psnorm the distribution function,
qsnorm the quantile function,
rsnorm generates random deviates.
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
## 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 0 1 2 3 4 5