| 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 |
lower.tail |
logical; if |
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 is the cumulative distribution function, and
qlnorm is the quantile function of the log-normal distribution.
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)