Lognormal {stats}  R Documentation 
The Log Normal Distribution
Description
Density, distribution function, quantile function and random
generation for the log normal distribution whose logarithm has mean
equal to meanlog
and standard deviation equal to sdlog
.
Usage
dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE)
plnorm(q, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)
qlnorm(p, meanlog = 0, sdlog = 1, lower.tail = TRUE, log.p = FALSE)
rlnorm(n, meanlog = 0, sdlog = 1)
Arguments
x , q 
vector of quantiles. 
p 
vector of probabilities. 
n 
number of observations. If 
meanlog , sdlog 
mean and standard deviation of the distribution
on the log scale with default values of 
log , log.p 
logical; if TRUE, probabilities p are given as log(p). 
lower.tail 
logical; if TRUE (default), probabilities are

Details
The log normal distribution has density
f(x) = \frac{1}{\sqrt{2\pi}\sigma x} e^{(\log(x)  \mu)^2/2 \sigma^2}%
where \mu
and \sigma
are the mean and standard
deviation of the logarithm.
The mean is E(X) = exp(\mu + 1/2 \sigma^2)
,
the median is med(X) = exp(\mu)
, 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
).
Value
dlnorm
gives the density,
plnorm
gives the distribution function,
qlnorm
gives the quantile function, and
rlnorm
generates random deviates.
The length of the result is determined by n
for
rlnorm
, and is the maximum of the lengths of the
numerical arguments for the other functions.
The numerical arguments other than n
are recycled to the
length of the result. Only the first elements of the logical
arguments are used.
Note
The cumulative hazard H(t) =  \log(1  F(t))
is plnorm(t, r, lower = FALSE, log = TRUE)
.
Source
dlnorm
is calculated from the definition (in ‘Details’).
[pqr]lnorm
are based on the relationship to the normal.
Consequently, they model a single point mass at exp(meanlog)
for the boundary case sdlog = 0
.
References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 14. Wiley, New York.
See Also
Distributions for other standard distributions, including
dnorm
for the normal distribution.
Examples
dlnorm(1) == dnorm(0)