R/ghypMeanVarMode.R

In GeneralizedHyperbolic: The Generalized Hyperbolic Distribution

### Function to calculate the theoretical mean of a
### generalized hyperbolic distribution given its parameters.
ghypMean <- function(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
                     param = c(mu, delta, alpha, beta, lambda)) {

  param <- as.numeric(param)

  if (length(param) == 4)
    param <- c(param, 1)

  ## check parameters
  parResult <- ghypCheckPars(param)
  case <- parResult$case
  errMessage <- parResult$errMessage

  if (case == "error")
    stop(errMessage)

  mu <- param[1]
  delta <- param[2]
  alpha <- param[3]
  beta <- param[4]
  lambda <- param[5]

  gamma <- sqrt(alpha^2 - beta^2)

  mn <- mu + delta*beta*besselRatio(delta*gamma, lambda, 1)/gamma
  mn
} ## End of ghypMean()

### Function to calculate the theoretical variance of a
### generalized hyperbolic distribution given its parameters.
ghypVar <- function(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
                    param = c(mu, delta, alpha, beta, lambda)) {

  param <- as.numeric(param)

  if (length(param) == 4)
    param <- c(param, 1)

  ## check parameters
  parResult <- ghypCheckPars(param)
  case <- parResult$case
  errMessage <- parResult$errMessage

  if (case == "error")
    stop(errMessage)

  var <- ghypMom(2, param = param, momType = "central")
  var
} ## End of ghypVar()

### Function to calculate the theoretical skewness of a
### generalized hyperbolic distribution given its parameters.
ghypSkew <- function(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
                     param = c(mu, delta, alpha, beta, lambda)) {

  param <- as.numeric(param)

  if (length(param) == 4)
    param <- c(param, 1)

  ## check parameters
  parResult <- ghypCheckPars(param)
  case <- parResult$case
  errMessage <- parResult$errMessage

  if (case == "error")
    stop(errMessage)

  skew <- ghypMom(3, param = param, momType = "central")/
                 (ghypVar(param = param)^(3/2))
  skew
} ## End of ghypSkew()

### Function to calculate the theoretical kurtosis of a
### generalized hyperbolic distribution given its parameters.
ghypKurt <- function(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
                     param = c(mu, delta, alpha, beta, lambda)) {

  param <- as.numeric(param)

  if (length(param) == 4)
    param <- c(param, 1)

  ## check parameters
  parResult <- ghypCheckPars(param)
  case <- parResult$case
  errMessage <- parResult$errMessage

  if (case == "error")
    stop(errMessage)

  kurt <- ghypMom(4, param = param, momType = "central")/
                 (ghypVar(param = param)^2) - 3
  kurt
} ## End of ghypKurt()

### Function to calculate the theoretical mode point of a
### generalized hyperbolic distribution given its parameters.
ghypMode <- function(mu = 0, delta = 1, alpha = 1, beta = 0, lambda = 1,
                     param = c(mu, delta, alpha, beta, lambda)) {

  param <- as.numeric(param)

  if (length(param) == 4)
    param <- c(param, 1)

  ## check parameters
  parResult <- ghypCheckPars(param)
  case <- parResult$case
  errMessage <- parResult$errMessage

  if (case == "error")
    stop(errMessage)

  modeFun <- function(x) {
    log(dghyp(x, param = param))
  }
  mu <- param[1]
  delta <- param[2]
  xHigh <- mu + delta
  while (dghyp(xHigh, param = param) > dghyp(mu, param = param)) {
      xHigh <- xHigh + delta
  }
  xLow <- mu - delta
  while (dghyp(xLow, param = param) > dghyp(mu, param = param)) {
      xLow <- xLow - delta
  }
  range <- c(xLow, xHigh)
  optResult <- optimize(f = modeFun, interval = range, maximum = TRUE)
  mode <- optResult$maximum
  mode
} ## End of ghypMode()