Distributacalcul (version 0.2.2)

V_llogis: Variance of the Loglogistic distribution

Description

Variance of the Loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\).

Usage

V_llogis(shape, rate = 1/scale, scale = 1/rate)

Arguments

shape

shape parameter \(\tau\), must be positive integer.

rate

alternative parameterization the scale parameter, rate = 1 / scale.

scale

\(\lambda\) rate parameter, must be positive.

Value

Function :

• E_llogis gives the expected value.

• V_llogis gives the variance.

• kthmoment_llogis gives the kth moment.

• Etronq_llogis gives the truncated mean.

• SL_llogis gives the stop-loss.

• Elim_llogis gives the limited mean.

• Mexcess_llogis gives the mean excess loss.

• TVaR_llogis gives the Tail Value-at-Risk.

• VaR_llogis gives the Value-at-Risk.

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

Details

The Loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\) has density: $$\frac{\tau \lambda^\tau x^{\tau -1}}{(\lambda^{\tau }+x^{\tau })^{2}}$$ for \(x \in \mathcal{R}^+\), \(\lambda, \tau > 0\).

See Also

Other Loglogistic Distribution: E_llogis(), Elim_llogis(), Etronq_llogis(), Mexcess_llogis(), SL_llogis(), TVaR_llogis(), VaR_llogis(), kthmoment_llogis()

Examples

# NOT RUN {
# With scale parameter
V_llogis(shape = 3, scale = 5)

# With rate parameter
V_llogis(shape = 3, rate = 0.2)

# Equivalently :
kthmoment_llogis(k = 2, shape = 3, rate = 0.2) - kthmoment_llogis(k = 1, shape = 3, rate = 0.2)^2

# }