# lognormal: Lognormal Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Maximum likelihood estimation of the (univariate) lognormal distribution.

## Usage

 `1` ```lognormal(lmeanlog = "identitylink", lsdlog = "loglink", 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`.

T. W. Yee

## References

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

`Lognormal`, `uninormal`, `CommonVGAMffArguments`, `simulate.vlm`.

## Examples

 ```1 2 3 4 5 6 7``` ```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) ```

### Example output

```Loading required package: stats4
VGLM    linear loop  1 :  loglikelihood = -3256.7497
VGLM    linear loop  2 :  loglikelihood = -2845.898
VGLM    linear loop  3 :  loglikelihood = -2548.6544
VGLM    linear loop  4 :  loglikelihood = -2416.0695
VGLM    linear loop  5 :  loglikelihood = -2395.051
VGLM    linear loop  6 :  loglikelihood = -2394.5967
VGLM    linear loop  7 :  loglikelihood = -2394.5965
VGLM    linear loop  8 :  loglikelihood = -2394.5965
VGLM    linear loop  1 :  loglikelihood = -1880.2594
VGLM    linear loop  2 :  loglikelihood = -1873.0471
VGLM    linear loop  3 :  loglikelihood = -1872.9743
VGLM    linear loop  4 :  loglikelihood = -1872.9742
VGLM    linear loop  5 :  loglikelihood = -1872.9742
meanlog loge(sdlog)
(Intercept) 0.9936615   -1.026091
x2          2.0215035    0.000000
meanlog loge(sdlog)
(Intercept) 1.005146   -1.042064
x2          0.000000    1.018054
```

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.