Normal distribution

expValNorm(mean, sd)

varNorm(mean, sd)

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

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

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

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

VatRNorm(kap, mean = 0, sd = 1)

TVatRNorm(kap, mean = 0, sd = 1)

mgfNorm(t, mean = 0, sd = 1)

## Arguments

mean

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

sd

standard deviation $$\sigma$$, must be positive.

d

cut-off value.

less.than.d

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

kap

probability.

t

t.

## Value

Function :

• expValNorm gives the expected value.

• varNorm gives the variance.

• expValLimNorm gives the limited mean.

• expValTruncNorm gives the truncated mean.

• stopLossNorm gives the stop-loss.

• meanExcessNorm gives the mean excess loss.

• VatRNorm gives the Value-at-Risk.

• TVatRNorm gives the Tail Value-at-Risk.

• mgfNorm gives the moment generating function (MGF).

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 $$x \in \mathcal{R}$$, $$\mu \in \mathcal{R}, \sigma > 0$$.

## Note

Function VatRNorm is a wrapper of the qnorm function from the stats package.

## Examples

expValNorm(mean = 3, sd = 5)
#> [1] 3

varNorm(mean = 3, sd = 5)
#> [1] 25

expValLimNorm(d = 2, mean = 2, sd = 5)
#> [1] 0.005288598

expValTruncNorm(d = 2, mean = 2, sd = 5)
#> [1] -0.9947114

stopLossNorm(d = 2, mean = 2, sd = 5)
#> [1] 0.005288598

meanExcessNorm(d = 2, mean = 2, sd = 5)
#> [1] 0.0105772

VatRNorm(kap = 0.8, mean = 3, sd = 5)
#> [1] 7.208106

TVatRNorm(kap = 0.8, mean = 2, sd = 5)
#> [1] 8.999048

mgfNorm(t = 1, mean = 3, sd = 5)
#> [1] 5389698