Lognormal {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 *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*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*).

### 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)

[Package

*stats* version 2.9.0

Index]