Lognormal               package:stats               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), the median is
     med(X) = exp(mu), 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)'.

Source:

     'dlnorm' is calculated from the definition (in 'Details').
     '[pqr]lnorm' are based on the relationship to the normal.

References:

     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.

Examples:

     dlnorm(1) == dnorm(0)

