# R/ghypMeanVarMode.R In sjp/GeneralizedHyperbolic: The generalized hyperbolic distribution

#### Documented in ghypKurtghypMeanghypModeghypSkewghypVar

```### 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)

mu + delta * beta * besselRatio(delta * gamma, lambda, 1) / gamma
} ## 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")
return(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))
return(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
return(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))
}

start <- ghypMean(param = param)
optResult <- optim(start, modeFun,
control = list(fnscale = -1, maxit = 1000),
method = "BFGS")

mode <- ifelse(optResult\$convergence == 0, optResult\$par, NA)
mode
} ## End of ghypMode()
```
sjp/GeneralizedHyperbolic documentation built on May 26, 2017, 10:13 a.m.