VGAM (version 1.1-14)

lognormal: Lognormal Distribution

Description

Maximum likelihood estimation of the (univariate) lognormal distribution.

Usage

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

Value

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

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

References

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

See Also

Lognormal, uninormal, CommonVGAMffArguments, simulate.vlm.

Examples

ldata2 <- data.frame(x2 = runif(nn <- 1000))
ldata2 <- transform(ldata2, y1 = rlnorm(nn, 1 + 2 * x2, sd = exp(-1)),
                            y2 = rlnorm(nn, 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)