Lognormal                package:base                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 `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].

Details:

     The log normal distribution has density

   f(x) = 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), 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)'.

See Also:

     `dnorm' for the normal distribution.

Examples:

     dlnorm(1) == dnorm(0)
     x <- rlnorm(1000)       # not yet always :
     all(abs(x  -  qlnorm(plnorm(x))) < 1e4 * .Machine$double.eps * x)

