Distributacalcul (version 0.2.2)

Etronq_norm: Truncated mean of the Normal distribution

Description

Truncated mean of the Normal distribution with mean \(\mu\) and variance \(\sigma\).

Usage

Etronq_norm(d, mean = 0, sd = 1, less.than.d = TRUE)

Arguments

d

cut-off value.

mean

mean (location) parameter \(\mu\).

sd

standard deviation \(\sigma\), must be positive.

less.than.d

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

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: $$\frac{1}{\sqrt{2\pi}\sigma}\textrm{e}^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2}$$ for \(x \in \mathcal{R}\), \(\mu \in \mathcal{R}, \sigma > 0\).

See Also

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

Examples

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

# }