bilogistic {VGAM} | R Documentation |
Bivariate Logistic Distribution Family Function
Description
Estimates the four parameters of the bivariate logistic distribution by maximum likelihood estimation.
Usage
bilogistic(llocation = "identitylink", lscale = "loglink",
iloc1 = NULL, iscale1 = NULL, iloc2 = NULL, iscale2 =
NULL, imethod = 1, nsimEIM = 250, zero = NULL)
Arguments
llocation |
Link function applied to both location parameters
|
lscale |
Parameter link function applied to both
(positive) scale parameters |
iloc1 , iloc2 |
Initial values for the location parameters.
By default, initial values are chosen internally using
|
iscale1 , iscale2 |
Initial values for the scale parameters.
By default, initial values are chosen internally using
|
imethod |
An integer with value |
nsimEIM , zero |
See |
Details
The four-parameter bivariate logistic distribution has a density that can be written as
where and
are the scale parameters,
and
and
are the location parameters.
Each of the two responses are unbounded, i.e.,
.
The mean of
is
etc.
The fitted values are returned in a 2-column matrix.
The cumulative distribution function is
The marginal distribution of is
By default, ,
,
,
are the linear/additive
predictors.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
,
rrvglm
and vgam
.
Author(s)
T. W. Yee
References
Gumbel, E. J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association, 56, 335–349.
Castillo, E., Hadi, A. S., Balakrishnan, N. and Sarabia, J. S. (2005). Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience.
See Also
Examples
## Not run:
ymat <- rbilogis(n <- 50, loc1 = 5, loc2 = 7, scale2 = exp(1))
plot(ymat)
bfit <- vglm(ymat ~ 1, family = bilogistic, trace = TRUE)
coef(bfit, matrix = TRUE)
Coef(bfit)
head(fitted(bfit))
vcov(bfit)
head(weights(bfit, type = "work"))
summary(bfit)
## End(Not run)