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)mean (location) parameter \(\mu\).
standard deviation \(\sigma\), must be positive.
cut-off value.
logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
probability.
t.
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.
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 \(x \in \mathcal{R}\), \(\mu \in \mathcal{R}, \sigma > 0\).
Function VatRNorm is a wrapper of the qnorm
function from the stats package.
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