Distributacalcul (version 0.2.2)

V_IG: Variance of the Inverse Gaussian distribution

Description

Variance of the Inverse Gaussian distribution with mean $\mu$ and shape parameter $\beta$.

Usage

V_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: E_IG(), Elim_IG(), Etronq_IG(), MGF_IG(), Mexcess_IG(), SL_IG(), TVaR_IG(), VaR_IG()

Examples

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

# }