Distributacalcul (version 0.2.2)

Elim_norm: Limited mean of the Normal distribution

Description

Limited mean of the Normal distribution with mean $\mu$ and variance $\sigma$.

Usage

Elim_norm(d, mean = 0, sd = 1)

Arguments

d

cut-off value.

mean

mean (location) parameter $\mu$.

sd

standard deviation $\sigma$, must be positive.

Value

Function :

• MGF_norm gives the moment generating function (MGF).

• E_norm gives the expected value.

• V_norm gives the variance.

• Etronq_norm gives the truncated mean.

• SL_norm gives the stop-loss.

• Elim_norm gives the limited mean.

• Mexcess_norm gives the mean excess loss.

• TVaR_norm gives the Tail Value-at-Risk.

• VaR_norm gives the Value-at-Risk.

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

Details

The Normal distribution with mean $\mu$ and standard deviation $\sigma$ has density: $$\frac{1}{\sqrt{2\pi }\sigma }{\text{e}}^{-\frac{1}{2}{\left(\frac{x-\mu }{\sigma }\right)}^2}$$ for $x\in \mathcal{R}$, $\mu \in \mathcal{R},\sigma >0$.

See Also

Other Normal distribution: E_norm(), Etronq_norm(), MGF_norm(), Mexcess_norm(), SL_norm(), TVaR_norm(), V_norm(), VaR_norm()

Examples

# NOT RUN {
Elim_norm(d = 2, mean = 2, sd = 5)

# }