R/distrG-aux.R

In tukeyGH: Tukey's g-and-h Probability Distribution

# g transformation
# NOTE: all arguments must be valid and vectorised
Tg <- function(x, a, b, g) {
  # g
  pos <- which(g != 0)
  x[pos] <- (exp(g[pos] * x[pos]) - 1) / g[pos]
  
  # Location and scale
  x <- a + b * x
  
  # Output
  return(x)
}



# Inverse of the g transformation
# NOTE: all arguments must be valid and vectorised
inv_Tg <- function(x, a, b, g) {
  # Computation
  x <- (x - a) / b
  pos <- which(g != 0)
  x[pos] <- log(pmax(1 + g[pos] * x[pos], 0)) / g[pos]
  
  # Output
  return(x)
}



# Derivative of g transformation
# NOTE: all arguments must be valid and vectorised
deriv_Tg <- function(x, b, g, log = FALSE) {
  out <- g * x
  out[g == 0] <- 0
  
  if (log == TRUE) {
    out <- log(b) + out
  } else {
    out <- b * exp(out)
  }
  
  return(out)
}



# log-likelihood function of g
loglikG <- function(theta, x) {
  dg(x, a = theta[1], b = theta[2], g = theta[3], log = TRUE) %>%
    sum() %>%
    max(-.Machine$double.xmax, na.rm = TRUE) %>%
    return()
}