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.
Extends
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
concept
- absolutely continuous distribution
- Log-Normal distribution
- S4 distribution class
See Also
LnormParameter-class
AbscontDistribution-class
Reals-class
rlnorm
Examples
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.
meanlog(L) # meanlog of this distribution is 1.
meanlog(L) <- 2 # meanlog of this distribution is now 2.