Lnorm-class | R Documentation |
The log normal distribution has density
d(x) = \frac{1}{\sqrt{2\pi}\sigma x} e^{-(\log(x) - \mu)^2/2 \sigma^2}%
where \mu
, by default =0
, and \sigma
, by default =1
, are the mean and standard
deviation of the logarithm.
C.f. rlnorm
Objects can be created by calls of the form Lnorm(meanlog, sdlog)
.
This object is a log normal distribution.
img
Object of class "Reals"
: The space of the image of this distribution has got dimension 1
and the name "Real Space".
param
Object of class "LnormParameter"
: the parameter of this distribution (meanlog and sdlog),
declared at its instantiation
r
Object of class "function"
: generates random numbers (calls function rlnorm
)
d
Object of class "function"
: density function (calls function dlnorm
)
p
Object of class "function"
: cumulative function (calls function plnorm
)
q
Object of class "function"
: inverse of the cumulative function (calls function qlnorm
)
.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.
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
signature(.Object = "Lnorm")
: initialize method
signature(object = "Lnorm")
: returns the slot meanlog
of the parameter of the distribution
signature(object = "Lnorm")
: modifies the slot meanlog
of the parameter of the distribution
signature(object = "Lnorm")
: returns the slot sdlog
of the parameter of the distribution
signature(object = "Lnorm")
: modifies the slot sdlog
of the parameter of the distribution
signature(e1 = "Lnorm", e2 = "numeric")
:
For the Lognormal distribution we use its closedness under positive scaling transformations.
The mean is E(X) = exp(\mu + 1/2 \sigma^2)
, and the variance
Var(X) = exp(2\mu + \sigma^2)(exp(\sigma^2) - 1)
and
hence the coefficient of variation is
\sqrt{exp(\sigma^2) - 1}
which is
approximately \sigma
when that is small (e.g., \sigma < 1/2
).
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
LnormParameter-class
AbscontDistribution-class
Reals-class
rlnorm
L <- Lnorm(meanlog=1,sdlog=1) # L is a lnorm distribution with mean=1 and sd=1.
r(L)(1) # one random number generated from this distribution, e.g. 3.608011
d(L)(1) # Density of this distribution is 0.2419707 for x=1.
p(L)(1) # Probability that x<1 is 0.1586553.
q(L)(.1) # Probability that x<0.754612 is 0.1.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
meanlog(L) # meanlog of this distribution is 1.
meanlog(L) <- 2 # meanlog of this distribution is now 2.
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