R: Class "Norm"

Norm-class {distr} | R Documentation

## Class "Norm"

### Description

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 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

### Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de

### See Also

`UniNormParameter-class` `AbscontDistribution-class` `Reals-class` `rnorm`

### Examples

    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)).

[Package distr version 2.8.0 Index]