distr (version 2.9.5)

Norm-class: Class "Norm"

Description

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

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

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

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)).