Class "Norm"
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.
imgObject of class "Reals": The domain of this distribution has got dimension 1
and the name "Real Space".
paramObject of class "UniNormParameter": the parameter of this distribution (mean and sd),
declared at its instantiation
rObject of class "function": generates random numbers (calls function rnorm)
dObject of class "function": density function (calls function dnorm)
pObject of class "function": cumulative function (calls function pnorm)
qObject of class "function": inverse of the cumulative function (calls function qnorm)
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject 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.
signature(.Object = "Norm"): initialize method
signature(object = "Norm"): returns the slot mean of the parameter of the distribution
signature(object = "Norm"): modifies the slot mean of the parameter of the distribution
signature(object = "Norm"): returns the slot sd of the parameter of the distribution
signature(object = "Norm"): modifies the slot sd of the parameter of the distribution
further arithmetic methods see operators-methods
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
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)).
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