IG.Rd
Inverse Gaussian distribution with mean \(\mu\) and shape parameter \(\beta\).
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)
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 |
kap | probability. |
t | t. |
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.
The Inverse Gaussian distribution with
Function VatRIG is a wrapper for the qinvgauss
function from the statmod package.
expValIG(mean = 2, shape = 5)#> [1] 2varIG(mean = 2, shape = 5)#> [1] 10expValLimIG(d = 2, mean = 2, shape = 5)#> [1] 1.083508expValTruncIG(d = 2, mean = 2, shape = 5)#> [1] -0.3747381stopLossIG(d = 2, mean = 2, shape = 5)#> [1] 0.916492meanExcessIG(d = 2, mean = 2, shape = 5)#> [1] 3.383425VatRIG(kap = 0.99, mean = 2, shape = 5)#> [1] 15.7671TVatRIG(kap = 0.99, mean = 2, shape = 5)#> [1] 8861.182mgfIG(t = 1, mean = 2, shape = .5)#> [1] 54.59815