# IG: Inverse Gaussian Distribution In Distributacalcul: Probability Distribution Functions

## Description

Inverse Gaussian distribution with mean mu and shape parameter beta.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```expValIG(mean, shape = dispersion * mean^2, dispersion = shape/mean^2) varIG(mean, shape = dispersion * mean^2, dispersion = shape/mean^2) expValLimIG(d, mean, shape = dispersion * mean^2, dispersion = shape/mean^2) expValTruncIG( d, mean, shape = dispersion * mean^2, dispersion = shape/mean^2, less.than.d = TRUE ) stopLossIG(d, mean, shape = dispersion * mean^2, dispersion = shape/mean^2) meanExcessIG(d, mean, shape = dispersion * mean^2, dispersion = shape/mean^2) VatRIG(kap, mean, shape = dispersion * mean^2, dispersion = shape/mean^2) TVatRIG(kap, mean, shape = dispersion * mean^2, dispersion = shape/mean^2) mgfIG(t, mean, shape = dispersion * mean^2, dispersion = shape/mean^2) ```

## Arguments

 `mean` mean (location) parameter mu, must be positive. `shape` shape parameter beta, must be positive `dispersion` alternative parameterization to the shape parameter, dispersion = 1 / rate. `d` cut-off value. `less.than.d` logical; if `TRUE` (default) truncated mean for values <= d, otherwise, for values > d. `kap` probability. `t` t.

## Details

The Inverse Gaussian distribution with

## Value

Function :

• `expValIG` gives the expected value.

• `varIG` gives the variance.

• `expValLimIG` gives the limited mean.

• `expValTruncIG` gives the truncated mean.

• `stopLossIG` gives the stop-loss.

• `meanExcessIG` gives the mean excess loss.

• `VatRIG` gives the Value-at-Risk.

• `TVatRIG` gives the Tail Value-at-Risk.

• `mgfIG` gives the moment generating function (MGF).

Invalid parameter values will return an error detailing which parameter is problematic.

## Note

Function VatRIG is a wrapper for the `qinvgauss` function from the statmod package.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```expValIG(mean = 2, shape = 5) varIG(mean = 2, shape = 5) expValLimIG(d = 2, mean = 2, shape = 5) expValTruncIG(d = 2, mean = 2, shape = 5) stopLossIG(d = 2, mean = 2, shape = 5) meanExcessIG(d = 2, mean = 2, shape = 5) VatRIG(kap = 0.99, mean = 2, shape = 5) TVatRIG(kap = 0.99, mean = 2, shape = 5) mgfIG(t = 1, mean = 2, shape = .5) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.