Lognormal {stats}R Documentation

The Log Normal Distribution


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.

See Also

dnorm for the normal distribution.


dlnorm(1) == dnorm(0)

[Package stats version 2.5.0 Index]