Distributacalcul (version 0.4.0)

Norm: Normal Distribution

Description

Normal distribution

Usage

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)

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.

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.

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

Examples

expValNorm(mean = 3, sd = 5)

varNorm(mean = 3, sd = 5)

expValLimNorm(d = 2, mean = 2, sd = 5)

expValTruncNorm(d = 2, mean = 2, sd = 5)

stopLossNorm(d = 2, mean = 2, sd = 5)

meanExcessNorm(d = 2, mean = 2, sd = 5)

VatRNorm(kap = 0.8, mean = 3, sd = 5)

TVatRNorm(kap = 0.8, mean = 2, sd = 5)

mgfNorm(t = 1, mean = 3, sd = 5)