R/distr_laplace_meanscale.R

In gasmodel: Generalized Autoregressive Score Models

# LAPLACE DISTRIBUTION / MEAN-SCALE PARAMETRIZATION


# Parameters Function ----------------------------------------------------------
distr_laplace_meanscale_parameters <- function(n) {
  group_of_par_names <- c("mean", "scale")
  par_names <- c("mean", "scale")
  par_support <- c("real", "positive")
  res_parameters <- list(group_of_par_names = group_of_par_names, par_names = par_names, par_support = par_support)
  return(res_parameters)
}
# ------------------------------------------------------------------------------


# Density Function -------------------------------------------------------------
distr_laplace_meanscale_density <- function(y, f) {
  t <- nrow(f)
  m <- f[, 1, drop = FALSE]
  s <- f[, 2, drop = FALSE]
  res_density <- exp(-abs(y - m) / s) / (2 * s)
  return(res_density)
}
# ------------------------------------------------------------------------------


# Log-Likelihood Function ------------------------------------------------------
distr_laplace_meanscale_loglik <- function(y, f) {
  t <- nrow(f)
  m <- f[, 1, drop = FALSE]
  s <- f[, 2, drop = FALSE]
  res_loglik <- -log(2 * s) - abs(y - m) / s
  return(res_loglik)
}
# ------------------------------------------------------------------------------


# Mean Function ----------------------------------------------------------------
distr_laplace_meanscale_mean <- function(f) {
  t <- nrow(f)
  m <- f[, 1, drop = FALSE]
  s <- f[, 2, drop = FALSE]
  res_mean <- m
  return(res_mean)
}
# ------------------------------------------------------------------------------


# Variance Function ------------------------------------------------------------
distr_laplace_meanscale_var <- function(f) {
  t <- nrow(f)
  m <- f[, 1, drop = FALSE]
  s <- f[, 2, drop = FALSE]
  res_var <- 2 * s^2
  res_var <- array(res_var, dim = c(t, 1, 1))
  return(res_var)
}
# ------------------------------------------------------------------------------


# Score Function ---------------------------------------------------------------
distr_laplace_meanscale_score <- function(y, f) {
  t <- nrow(f)
  m <- f[, 1, drop = FALSE]
  s <- f[, 2, drop = FALSE]
  res_score <- matrix(0, nrow = t, ncol = 2L)
  res_score[, 1] <- sign(y - m) / s
  res_score[, 2] <- abs(y - m) / s^2 - 1 / s
  return(res_score)
}
# ------------------------------------------------------------------------------


# Fisher Information Function --------------------------------------------------
distr_laplace_meanscale_fisher <- function(f) {
  t <- nrow(f)
  m <- f[, 1, drop = FALSE]
  s <- f[, 2, drop = FALSE]
  res_fisher <- array(0, dim = c(t, 2L, 2L))
  res_fisher[, 1, 1] <- 1 / s^2
  res_fisher[, 2, 2] <- 1 / s^2
  return(res_fisher)
}
# ------------------------------------------------------------------------------


# Random Generation Function ---------------------------------------------------
distr_laplace_meanscale_random <- function(t, f) {
  m <- f[1]
  s <- f[2]
  u <- stats::runif(n = t, min = -1, max = 1)
  res_random <- m - s * sign(u) * log(1 - abs(u))
  res_random <- matrix(res_random, nrow = t, ncol = 1L)
  return(res_random)
}
# ------------------------------------------------------------------------------


# Starting Estimates Function --------------------------------------------------
distr_laplace_meanscale_start <- function(y) {
  y_mean <- mean(y, na.rm = TRUE)
  y_var <- stats::var(y, na.rm = TRUE)
  m <- y_mean
  s <- max(sqrt(y_var / 2), 1e-6)
  res_start <- c(m, s)
  return(res_start)
}
# ------------------------------------------------------------------------------