Density, distribution function, quantile function and random
generation for the log normal distribution whose logarithm has mean
meanlog and standard deviation equal to
1 2 3 4
vector of quantiles.
vector of probabilities.
number of observations. If
mean and standard deviation of the distribution
on the log scale with default values of
logical; if TRUE, probabilities p are given as log(p).
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
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))
-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
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.