R/nlMeanVarSkewKurt.R

In sjp/NormalLaplace: The Normal Laplace Distribution

### Mean function
nlMean <- function(mu = 0, sigma = 1, alpha = 1, beta = 1,
                   param = c(mu, sigma, alpha, beta)) {

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

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

  mu <- param[1]
  sigma <- param[2]
  alpha <- param[3]
  beta <- param[4]

  nlMean <- mu + 1/alpha - 1/beta

  return(nlMean)
}


### Variance function
nlVar <- function(mu = 0, sigma = 1, alpha = 1, beta = 1,
                  param = c(mu, sigma, alpha, beta)) {

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

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

  mu <- param[1]
  sigma <- param[2]
  alpha <- param[3]
  beta <- param[4]

  nlVar <- sigma^2 + 1/(alpha^2) + 1/(beta^2)

  return(nlVar)
}


### Skewness function
nlSkew <- function(mu = 0, sigma = 1, alpha = 1, beta = 1,
                   param = c(mu, sigma, alpha, beta)) {

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

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

  mu <- param[1]
  sigma <- param[2]
  alpha <- param[3]
  beta <- param[4]

  k2 <- nlVar(param = param)
  k3 <- 2/(alpha^3) - 2/(beta^3)

  nlSkew <- k3/(k2^(3/2))

  return(nlSkew)
}


### Kurtosis function
nlKurt <- function (mu = 0, sigma = 1, alpha = 1, beta = 1,
                    param = c(mu, sigma, alpha, beta)) {

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

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

  mu <- param[1]
  sigma <- param[2]
  alpha <- param[3]
  beta <- param[4]

  k2 <- nlVar(param = param)
  k4 <- 6/(alpha^4) + 6/(beta^4)
  nlKurt <- k4/(k2^2)

  return(nlKurt)
}