Description Objects from the Class Slots Extends Methods Author(s) See Also Examples

The normal distribution has density

*
f(x) = 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`

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

.
This object is a normal distribution.

`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.

Class `"AbscontDistribution"`

, directly.

Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.

Class `"Distribution"`

, by class `"AbscontDistribution"`

.

- -
`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

Thomas Stabla [email protected],

Florian Camphausen [email protected],

Peter Ruckdeschel [email protected],

Matthias Kohl [email protected]

`UniNormParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rnorm`

1 2 3 4 5 6 7 8 9 | ```
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.
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)).
``` |

```
Loading required package: startupmsg
:startupmsg> Utilities for Start-Up Messages (version 0.9.4)
:startupmsg>
:startupmsg> For more information see ?"startupmsg",
:startupmsg> NEWS("startupmsg")
Loading required package: sfsmisc
Loading required package: SweaveListingUtils
:SweaveListingUtils> Utilities for Sweave Together with
:SweaveListingUtils> TeX 'listings' Package (version
:SweaveListingUtils> 0.7.7)
:SweaveListingUtils>
:SweaveListingUtils> NOTE: Support for this package
:SweaveListingUtils> will stop soon.
:SweaveListingUtils>
:SweaveListingUtils> Package 'knitr' is providing the
:SweaveListingUtils> same functionality in a better
:SweaveListingUtils> way.
:SweaveListingUtils>
:SweaveListingUtils> Some functions from package 'base'
:SweaveListingUtils> are intentionally masked ---see
:SweaveListingUtils> SweaveListingMASK().
:SweaveListingUtils>
:SweaveListingUtils> Note that global options are
:SweaveListingUtils> controlled by
:SweaveListingUtils> SweaveListingoptions() ---c.f.
:SweaveListingUtils> ?"SweaveListingoptions".
:SweaveListingUtils>
:SweaveListingUtils> For more information see
:SweaveListingUtils> ?"SweaveListingUtils",
:SweaveListingUtils> NEWS("SweaveListingUtils")
:SweaveListingUtils> There is a vignette to this
:SweaveListingUtils> package; try
:SweaveListingUtils> vignette("ExampleSweaveListingUtils").
Attaching package: 'SweaveListingUtils'
The following objects are masked from 'package:base':
library, require
:distr> Object Oriented Implementation of Distributions (version
:distr> 2.6.2)
:distr>
:distr> Attention: Arithmetics on distribution objects are
:distr> understood as operations on corresponding random variables
:distr> (r.v.s); see distrARITH().
:distr>
:distr> Some functions from package 'stats' are intentionally masked
:distr> ---see distrMASK().
:distr>
:distr> Note that global options are controlled by distroptions()
:distr> ---c.f. ?"distroptions".
:distr>
:distr> For more information see ?"distr", NEWS("distr"), as well as
:distr> http://distr.r-forge.r-project.org/
:distr> Package "distrDoc" provides a vignette to this package as
:distr> well as to several extension packages; try
:distr> vignette("distr").
Attaching package: 'distr'
The following objects are masked from 'package:stats':
df, qqplot, sd
[1] 1.433609
[1] 0.3989423
[1] 0.5
[1] -0.2815516
[1] 1
```

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