lognormal {VGAM} | R Documentation

## Lognormal Distribution

### Description

Maximum likelihood estimation of the (univariate) lognormal distribution.

### Usage

    lognormal(lmeanlog = "identitylink", lsdlog = "loge", zero = "sdlog")

### Arguments

`lmeanlog, lsdlog` | Parameter link functions applied to the mean and (positive) sigma (standard deviation) parameter. Both of these are on the log scale. See `Links` for more choices.

`zero` | Specifies which linear/additive predictor is modelled as intercept-only. For `lognormal()`, the values can be from the set {1,2} which correspond to `mu`, `sigma`, respectively. See `CommonVGAMffArguments` for more information.

### Details

A random variable Y has a 2-parameter lognormal distribution if log(Y) is distributed N(mu, sigma^2). The expected value of Y, which is

E(Y) = exp(mu + 0.5 sigma^2)

and not mu, make up the fitted values. The variance of Y is

Var(Y) = [exp(sigma^2) -1] * exp(2 mu + sigma^2).

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, and `vgam`.

### Author(s)

T. W. Yee

### References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.

### See Also

`rlnorm`, `uninormal`, `CommonVGAMffArguments`, `simulate.vlm`.

### Examples

    ldata2 <- data.frame(x2 = runif(nn <- 1000))
    ldata2 <- transform(ldata2, y1 = rlnorm(nn, mean = 1 + 2 * x2, sd = exp(-1)),
                                y2 = rlnorm(nn, mean = 1, sd = exp(-1 + x2)))
    fit1 <- vglm(y1 ~ x2, lognormal(zero = 2), data = ldata2, trace = TRUE)
    fit2 <- vglm(y2 ~ x2, lognormal(zero = 1), data = ldata2, trace = TRUE)
    coef(fit1, matrix = TRUE)
    coef(fit2, matrix = TRUE)

[Package VGAM version 1.0-3 Index]