Norm: Normal Distribution In Distributacalcul: Probability Distribution Functions

Description

Normal distribution

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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.

Details

The Normal distribution with mean mu and standard deviation sigma has density:

f(x) = e^(-(1/2) ((x - mu)/sigma)^2) / ((2 pi)^(1/2) sigma

for x real, mu real, sigma > 0.

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.

Note

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

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.