dng

dng provides distribution and gradient functions for split-normal and split-t distributions. It includes density, distribution, quantile, random generation, moment, and analytical gradient routines implemented with Rcpp.

Installation

Install the CRAN release with:

install.packages("dng")

Install the development version from GitHub with:

remotes::install_github("feng-li/dng")

Split-Normal Distribution

library(dng)

n <- 3
mu <- c(0, 1, 2)
sigma <- c(1, 2, 3)
lmd <- c(1, 2, 3)

x <- rsplitn(n, mu, sigma, lmd)
d <- dsplitn(x, mu, sigma, lmd, logarithm = FALSE)
p <- psplitn(x, mu, sigma, lmd)
q <- qsplitn(p, mu, sigma, lmd)

all.equal(x, q)

Moment helpers are also available:

splitn_mean(mu, sigma, lmd)
splitn_var(sigma, lmd)
splitn_skewness(sigma, lmd)
splitn_kurtosis(lmd)

Gradients of the CDF and log-density are available through gsplitn():

gsplitn(
  x,
  list(mu = mu, sigma = sigma, lmd = lmd),
  parCaller = "mu",
  denscaller = c("u", "d")
)

Split-t Distribution

mu <- c(0, 1, 2)
df <- rep(10, 3)
phi <- c(0.5, 1, 2)
lmd <- c(1, 2, 3)

x <- rsplitt(n, mu, df, phi, lmd)
d <- dsplitt(x, mu, df, phi, lmd, logarithm = FALSE)
p <- psplitt(x, mu, df, phi, lmd)
q <- qsplitt(p, mu, df, phi, lmd)

all.equal(x, q)

Moment helpers are also available:

splitt_mean(mu, df, phi, lmd)
splitt_var(df, phi, lmd)
splitt_skewness(df, phi, lmd)
splitt_kurtosis(df, phi, lmd)

Gradients of the CDF and log-density are available through gsplitt():

gsplitt(
  x,
  list(mu = mu, df = df, phi = phi, lmd = lmd),
  parCaller = "mu",
  denscaller = c("u", "d")
)

Reference

Li, F., Villani, M., and Kohn, R. (2010). Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities. Journal of Statistical Planning and Inference, 140(12), 3638-3654. https://doi.org/10.1016/j.jspi.2010.04.031

License

GPL (>= 2)