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)vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length
is taken to be the number required.
mean and standard deviation of the distribution
on the log scale with default values of 0 and 1 respectively.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
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 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., \(\sigma < 1/2\)).
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.