| lognormal {VGAM} | R Documentation |
Maximum likelihood estimation of the (univariate) lognormal distribution.
lognormal(lmeanlog = "identity", lsdlog = "loge",
emeanlog=list(), esdlog=list(), zero = NULL)
lognormal3(lmeanlog = "identity", lsdlog = "loge",
emeanlog=list(), esdlog=list(),
powers.try = (-3):3, delta = NULL, zero = NULL)
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.
|
emeanlog, esdlog |
List. Extra argument for each of the links.
See earg in Links for general information.
|
zero |
An integer-valued vector specifying which
linear/additive predictors are modelled as intercepts only.
For lognormal(),
the values must be from the set {1,2} which correspond to
mu, sigma, respectively.
For lognormal3(),
the values must be from the set {1,2,3} where 3 is for
λ.
|
powers.try |
Numerical vector. The initial lambda is chosen
as the best value from min(y) - 10^powers.try where
y is the response.
|
delta |
Numerical vector. An alternative method for
obtaining an initial lambda. Here, delta = min(y)-lambda.
If given, this supersedes the powers.try argument.
The value must be positive.
|
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.
A random variable Y has a 3-parameter lognormal distribution if log(Y-lambda) is distributed N(mu, sigma^2). Here, lambda < Y. The expected value of Y, which is
E(Y) = lambda + exp(mu + 0.5 sigma^2)
and not mu, make up the fitted values.
lognormal() and lognormal3() fit the 2- and 3-parameter
lognormal distribution respectively. Clearly, if the location
parameter lambda=0 then both distributions coincide.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
T. W. Yee
Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ: Wiley-Interscience.
y = rlnorm(n <- 1000, meanlog=1.5, sdlog=exp(-0.8)) fit = vglm(y ~ 1, lognormal, trace=TRUE) coef(fit, mat=TRUE) Coef(fit) x = runif(n <- 1000) y = rlnorm(n, mean=0.5, sd=exp(x)) fit = vglm(y ~ x, lognormal(zero=1), trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) lambda = 4 y = lambda + rlnorm(n <- 1000, mean=1.5, sd=exp(-0.8)) fit = vglm(y ~ 1, lognormal3, trace=TRUE) fit = vglm(y ~ 1, lognormal3, trace=TRUE, crit="c") coef(fit, mat=TRUE) Coef(fit) summary(fit)