trunclognormal  R Documentation 
Maximum likelihood estimate of the two–parameter lognormal distribution with lower/upper truncation.
trunclognormal(lmeanlog = "identitylink", lsdlog = "loglink",
min.support = 1e6, max.support = Inf, zero = "sdlog")
lmeanlog, lsdlog, zero 
Same as 
min.support, max.support 
Positive lower and upper truncation limits (recycled).

MLE of the two–parameter (univariate) lognormal distribution subject
to lower/upper truncation. All response values are greater
than min.support
and lower than max.support
.
Default values of min.support
, max.suppport
should
effectively reproduce lognormal
.
The truncated–lognormal density for a response Y
is
f(y; \mu, \sigma) = f_N(y; \mu, \sigma) /
[\Phi(\texttt{max.support}, \mu, \sigma) 
\Phi(\texttt{min.support},\mu, \sigma) ],
where f_N
is the ordinary lognormal density (see
lognormal
) and
\Phi
is the standard normal CDF.
The mean of Y, given by
\exp{(\mu + \sigma^2/2)} \cdot
[\Phi(((\log(\texttt{max.support})  \mu)/\sigma)  \sigma) 
\Phi(((\log(\texttt{min.support})  \mu)/\sigma)  \sigma) ] /
\Delta \Phi(\mu,\sigma),
with \Delta \Phi(\mu, \sigma) =
\Phi( (\log(\texttt{max.support})  \mu)/\sigma ) 
\Phi( (\log(\texttt{min.support})  \mu)/\sigma ),
are returned as the fitted values.
An object of class "vglmff"
(see vglmffclass
).
The object is used by modelling functions such as vglm
,
and vgam
.
Victor Miranda, Siqi (Vicky) Liu and Thomas W. Yee.
Nadarajah, S. and Kotz, S. (2003).
R
Programs for Computing Truncated Distributions.
Journal of Statistical Software, Code
Snippets,
16(2), 1–8.
Cohen, A.C. (1991) Truncated and Censored Samples: Theory and Applications, New York, USA. Marcel Dekker.
lognormal
,
uninormal
,
CommonVGAMffArguments
,
Lognormal
.
##########
set.seed(10470923)
nn < 3000
## Parameters
mysdlog < exp(1.5) # sdlog
LL < 3.5 # Lower bound
UL < 8.0 # Upper bound
## Truncated data
ldata2 < data.frame(x2 = runif(nn))
ldata2 < transform(ldata2, y1 = rtrunclnorm(nn, 1 + 1.5 * x2, mysdlog,
min.support = LL, max.support = UL))
# head(ldata2)
# hist(ldata2$y1, breaks = 22, col = "blue", xlim = c(0, 10))
##############################################################
# Fitting a truncated lognormal distribution  sd is intercept only
fit1 < vglm(y1 ~ x2, trunclognormal(zero = "sdlog", min.support = LL, max.support = UL),
data = ldata2, trace = TRUE)
coef(fit1, matrix = TRUE)
vcov(fit1)
##############################################################
# Fitting a truncated lognormal distribution  zero = NULL
fit2 < vglm(y1 ~ x2, trunclognormal(zero = NULL, min.support = LL, max.support = UL),
data = ldata2, trace = TRUE)
coef(fit2, matrix = TRUE)
vcov(fit2)
##############################################################
# Mimicking lognormal()
fit3 < vglm(y1 ~ x2, trunclognormal(zero = "sdlog"),
data = ldata2, trace = TRUE)
coef(fit3, mat = TRUE)
# Same as
fit3bis < vglm(y1 ~ x2, lognormal(zero = "sdlog"),
data = ldata2, trace = TRUE)
coef(fit3bis, mat = TRUE)
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