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

Arguments

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

Examples

Run this code

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)).

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