Lnorm-class
Class "Lnorm"
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
- Keywords
- distribution
Note
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., \(\sigma < 1/2\)).
Objects from the Class
Objects can be created by calls of the form Lnorm(meanlog, sdlog)
.
This object is a log normal distribution.
Slots
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 instantiationr
Object of class
"function"
: generates random numbers (calls functionrlnorm
)d
Object of class
"function"
: density function (calls functiondlnorm
)p
Object of class
"function"
: cumulative function (calls functionplnorm
)q
Object of class
"function"
: inverse of the cumulative function (calls functionqlnorm
).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
- initialize
signature(.Object = "Lnorm")
: initialize method- meanlog
signature(object = "Lnorm")
: returns the slotmeanlog
of the parameter of the distribution- meanlog<-
signature(object = "Lnorm")
: modifies the slotmeanlog
of the parameter of the distribution- sdlog
signature(object = "Lnorm")
: returns the slotsdlog
of the parameter of the distribution- sdlog<-
signature(object = "Lnorm")
: modifies the slotsdlog
of the parameter of the distribution- *
signature(e1 = "Lnorm", e2 = "numeric")
: For the Lognormal distribution we use its closedness under positive scaling transformations.
See Also
LnormParameter-class
AbscontDistribution-class
Reals-class
rlnorm
Examples
# NOT RUN {
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.
# }