leipnik {VGAM} | R Documentation |
Leipnik Regression Family Function
Description
Estimates the two parameters of a (transformed) Leipnik distribution by maximum likelihood estimation.
Usage
leipnik(lmu = "logitlink", llambda = logofflink(offset = 1),
imu = NULL, ilambda = NULL)
Arguments
lmu , llambda |
Link function for the |
imu , ilambda |
Numeric. Optional initial values for |
Details
The (transformed) Leipnik distribution has density function
where and
.
The mean is
(returned as the fitted values)
and the variance is
.
Jorgensen (1997) calls the above the transformed
Leipnik distribution, and if and
, then the distribution of
as a function of
and
is known as the
the (untransformed) Leipnik distribution. Here, both
and
are in
.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
,
rrvglm
and vgam
.
Note
Convergence may be slow or fail.
Until better initial value estimates are forthcoming try
assigning the argument ilambda
some numerical value if it
fails to converge. Currently, Newton-Raphson is implemented,
not Fisher scoring. Currently, this family function probably
only really works for intercept-only models, i.e., y ~
1
in the formula.
Author(s)
T. W. Yee
References
Jorgensen, B. (1997). The Theory of Dispersion Models. London: Chapman & Hall
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, 2nd edition, Volume 2, New York: Wiley. (pages 612–617).
See Also
Examples
ldata <- data.frame(y = rnorm(2000, 0.5, 0.1)) # Improper data
fit <- vglm(y ~ 1, leipnik(ilambda = 1), ldata, trace = TRUE)
head(fitted(fit))
with(ldata, mean(y))
summary(fit)
coef(fit, matrix = TRUE)
Coef(fit)
sum(weights(fit)) # Sum of the prior weights
sum(weights(fit, type = "work")) # Sum of the working weights