Distributacalcul (version 0.2.2)

E_IG: Expected value of the Inverse Gaussian distribution

Description

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

Usage

E_IG(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.

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: Elim_IG(), Etronq_IG(), MGF_IG(), Mexcess_IG(), SL_IG(), TVaR_IG(), V_IG(), VaR_IG()

Examples

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

# }