Distributacalcul (version 0.2.2)

Etronq_IG: Truncated mean of the Inverse Gaussian distribution

Description

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

Usage

Etronq_IG(
  d,
  mean,
  shape = dispersion * mean^2,
  dispersion = shape/mean^2,
  less.than.d = TRUE
)

Arguments

d

cut-off value.

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.

less.than.d

logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.

Value

Function :

• MGF_IG gives the moment generating function (MGF).

• E_IG gives the expected value.

• V_IG gives the variance.

• Etronq_IG gives the truncated mean.

• SL_IG gives the stop-loss.

• Elim_IG gives the limited mean.

• Mexcess_IG gives the mean excess loss.

• TVaR_IG gives the Tail Value-at-Risk.

• VaR_IG gives the Value-at-Risk.

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

Details

The Pareto distribution with rate parameter \(\lambda\) as well as shape parameter \(\alpha\) has density: $$f\left(x\right) = \frac{\alpha% \lambda^{\alpha}}{(\lambda + x)^{\alpha + 1}}$$ for \(x \in \mathcal{R}^+\), \(\alpha, \lambda > 0\).

See Also

Other Inverse Gaussian Distribution: E_IG(), Elim_IG(), MGF_IG(), Mexcess_IG(), SL_IG(), TVaR_IG(), V_IG(), VaR_IG()

Examples

# NOT RUN {
Etronq_IG(d = 2, mean = 2, shape = 5)

# }