# Lognormal {stats}

### 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
`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/(√(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).

### Values

`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 `n`

for `rlnorm`

, and is the maximum of the lengths of the numerical parameters for the other functions. The numerical parameters other than `n`

are recycled to the length of the result. Only the first elements of the logical parameters are used.

### 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

Distributions for other standard distributions, including `dnorm`

for the normal distribution.

Documentation reproduced from R 3.0.2. License: GPL-2.