wsgnstat

The skew generalised normal distribution on the line and its wrapping onto the circle: density, distribution and quantile functions, random generation, characteristic function, trigonometric moments, and estimation by trigonometric moments or maximum likelihood. The characteristic function is reached through absolutely convergent integrals rather than a series, so every shape parameter is available. The computation runs on a pure-C back-end shared with the Python package of the same name.

Installation

From CRAN, once accepted:

install.packages("wsgnstat")

The development version from GitHub:

# install.packages("remotes")
remotes::install_github("mtloots/wsgnstat", subdir = "wsgnstat")

Example

Simulate from a skew member of the wrapped family, estimate its parameters, and compare with the truth:

library(wsgnstat)
set.seed(1)
truth <- c(mu = 1, beta = 1.5, lam = 0.3)
theta <- rwsgn(1000, truth["mu"], truth["beta"], truth["lam"])
fit <- fit_wsgn_mle(theta)
round(rbind(truth = truth, estimate = fit$par), 3)
#>          mu beta   lam
#> truth     1 1.50 0.300
#> estimate  1 1.48 0.315

At shape 2 with lam = 0.5 the circular law is the wrapped normal with sigma = 1/sqrt(2), and its trigonometric moments are exactly exp(-p^2/4):

tm <- trig_moments(4, mu = 0, beta = 2, lam = 0.5)
rbind(engine = tm$A, closed_form = exp(-(1:4)^2 / 4))
#>                  [,1]      [,2]      [,3]       [,4]
#> engine      0.7788008 0.3678794 0.1053992 0.01831564
#> closed_form 0.7788008 0.3678794 0.1053992 0.01831564

The vignette, vignette("wsgnstat"), walks through the family, its reductions, estimation and an application to wind directions.