Lognormal {stats}  R Documentation 
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
.
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)
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

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
).
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.
The cumulative hazard H(t) =  \log(1  F(t))
is plnorm(t, r, lower = FALSE, log = TRUE)
.
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
.
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.
Distributions for other standard distributions, including
dnorm
for the normal distribution.
dlnorm(1) == dnorm(0)