Distributacalcul (version 0.4.0)

IG: Inverse Gaussian Distribution

Description

Inverse Gaussian distribution with mean \(\mu\) and shape parameter \(\beta\).

Usage

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)

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.

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

Examples

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)