# Norm-class

##### Class "Norm"

The normal distribution has density
$$
f(x) =
\frac{1}{\sqrt{2\pi}\sigma} e^{-(x-\mu)^2/2\sigma^2}$$
where \(\mu\) is the mean of the distribution and
\(\sigma\) the standard deviation.
C.f. `rnorm`

- Keywords
- distribution

##### Objects from the Class

Objects can be created by calls of the form `Norm(mean, sd)`

.
This object is a normal distribution.

##### Slots

`img`

Object of class

`"Reals"`

: The domain of this distribution has got dimension 1 and the name "Real Space".`param`

Object of class

`"UniNormParameter"`

: the parameter of this distribution (mean and sd), declared at its instantiation`r`

Object of class

`"function"`

: generates random numbers (calls function`rnorm`

)`d`

Object of class

`"function"`

: density function (calls function`dnorm`

)`p`

Object of class

`"function"`

: cumulative function (calls function`pnorm`

)`q`

Object of class

`"function"`

: inverse of the cumulative function (calls function`qnorm`

)`.withArith`

logical: used internally to issue warnings as to interpretation of arithmetics

`.withSim`

logical: used internally to issue warnings as to accuracy

`.logExact`

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

`.lowerExact`

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

`Symmetry`

object of class

`"DistributionSymmetry"`

; used internally to avoid unnecessary calculations.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### Methods

- -
`signature(e1 = "Norm", e2 = "Norm")`

- +
`signature(e1 = "Norm", e2 = "Norm")`

: For the normal distribution the exact convolution formulas are implemented thereby improving the general numerical approximation.- *
`signature(e1 = "Norm", e2 = "numeric")`

- +
`signature(e1 = "Norm", e2 = "numeric")`

: For the normal distribution we use its closedness under affine linear transformations.- initialize
`signature(.Object = "Norm")`

: initialize method- mean
`signature(object = "Norm")`

: returns the slot`mean`

of the parameter of the distribution- mean<-
`signature(object = "Norm")`

: modifies the slot`mean`

of the parameter of the distribution- sd
`signature(object = "Norm")`

: returns the slot`sd`

of the parameter of the distribution- sd<-
`signature(object = "Norm")`

: modifies the slot`sd`

of the parameter of the distribution

further arithmetic methods see operators-methods

##### See Also

`UniNormParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rnorm`

##### Examples

```
# NOT RUN {
N <- Norm(mean=1,sd=1) # N is a normal distribution with mean=1 and sd=1.
r(N)(1) # one random number generated from this distribution, e.g. 2.257783
d(N)(1) # Density of this distribution is 0.3989423 for x=1.
p(N)(1) # Probability that x<1 is 0.5.
q(N)(.1) # Probability that x<-0.2815516 is 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
mean(N) # mean of this distribution is 1.
sd(N) <- 2 # sd of this distribution is now 2.
M <- Norm() # M is a normal distribution with mean=0 and sd=1.
O <- M+N # O is a normal distribution with mean=1 (=1+0) and sd=sqrt(5) (=sqrt(2^2+1^2)).
# }
```

*Documentation reproduced from package distr, version 2.7.0, License: LGPL-3*