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)