| 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 length(n) > 1, the length
is taken to be the number required. |
meanlog, sdlog |
mean and standard deviation of the distribution
on the log scale with default values of 0 and 1 respectively. |
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/(sqrt(2 pi) sigma x) e^-((log x - mu)^2 / (2 sigma^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), 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 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 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.
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.
dnorm for the normal distribution.
dlnorm(1) == dnorm(0)