| Lognormal {base} | 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 to generate. |
meanlog, sdlog |
mean and standard deviation of the distribution on the log scale. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
If meanlog or sdlog are not specified they assume the
default values of 0 and 1 respectively.
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.
Value
dlnorm gives the density,
plnorm gives the distribution function,
qlnorm gives the quantile function, and
rlnorm generates random deviates.
Note
The cumulative hazard H(t) = - \log(1 - F(t))
is -plnorm(t, r, lower = FALSE, log = TRUE).
See Also
dnorm for the normal distribution.
Examples
dlnorm(1) == dnorm(0)
x <- rlnorm(1000) # not yet always :
all(abs(x - qlnorm(plnorm(x))) < 1e4 * .Machine$double.eps * x)