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)).