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

#### Documented in gigKurtgigMeangigModegigSkewgigVar

```### Function to calculate the theoretical mean of a
### generalized inverse Gaussian distribution given its parameters.
gigMean <- function(chi = 1, psi = 1, lambda = 1,
param = c(chi, psi, lambda)) {

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

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

param <- as.numeric(param)
chi <- param[1]
psi <- param[2]
lambda <- param[3]
omega <- sqrt(chi * psi)
eta <- sqrt(chi / psi)
eta * besselRatio(omega, lambda, 1)
} ## End of gigMean()

### Function to calculate the theoretical variance of a
### generalized inverse Gaussian distribution given its parameters.
gigVar <- function(chi = 1, psi = 1, lambda = 1,
param = c(chi, psi, lambda)) {

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

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

m1 <- gigMean(param = param)
var <- gigMom(2, param = param, about = m1)
return(var)
} ## End of gigVar()

### Function to calculate the theoretical skewness of a
### generalized inverse Gaussian distribution given its parameters.
gigSkew <- function(chi = 1, psi = 1, lambda = 1,
param = c(chi, psi, lambda)) {

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

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

m1 <- gigMean(param = param)
skew <- gigMom(3, param = param, about = m1) / (gigVar(param = param)^(3 / 2))
return(skew)
} ## End of gigSkew()

### Function to calculate the theoretical kurtosis of a
### generalized inverse Gaussian distribution given its parameters.
gigKurt <- function(chi = 1, psi = 1, lambda = 1,
param = c(chi, psi, lambda)) {

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

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

m1 <- gigMean(param = param)
kurt <- gigMom(4, param = param, about = m1) / (gigVar(param = param)^2) - 3
return(kurt)
} ## End of gigKurt()

### Function to calculate the theoretical mode point of a
### generalized inverse Gaussian distribution given its parameters.
gigMode <- function(chi = 1, psi = 1, lambda = 1,
param = c(chi, psi, lambda)) {

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

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

param <- as.numeric(param)
chi <- param[1]
psi <- param[2]
lambda <- param[3]
(lambda - 1 + sqrt((lambda - 1)^2 + chi * psi)) / psi
} ## End of gigMode()
```
sjp/GeneralizedHyperbolic documentation built on May 26, 2017, 10:13 a.m.