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 P[X ≤ x], otherwise, P[X > x]. |
The log normal distribution has density
f(x) = 1/(√(2 π) σ x) e^-((log x - μ)^2 / (2 σ^2))
where μ and σ are the mean and standard deviation of the logarithm. The mean is E(X) = exp(μ + 1/2 σ^2), the median is med(X) = exp(μ), and the variance Var(X) = exp(2*μ + σ^2)*(exp(σ^2) - 1) and hence the coefficient of variation is sqrt(exp(σ^2) - 1) which is approximately σ when that is small (e.g., σ < 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)