| 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.
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.
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
dnorm for the normal distribution.
Examples
dlnorm(1) == dnorm(0)