Bivariate Logistic Distribution Family Function
Estimates the four parameters of the bivariate logistic distribution by maximum likelihood estimation.
bilogistic(llocation = "identitylink", lscale = "loglink",
iloc1 = NULL, iscale1 = NULL, iloc2 = NULL, iscale2 = NULL,
imethod = 1, nsimEIM = 250, zero = NULL)llocation |
Link function applied to both location parameters
l1 and l2.
See |
lscale |
Parameter link function applied to both
(positive) scale parameters s1 and s2.
See |
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 |
The four-parameter bivariate logistic distribution has a density that can be written as
f(y1,y2;l1,s1,l2,s2) = 2 * exp[-(y1-l1)/s1 - (y1-l1)/s1] / [s1 * s2 * ( 1 + exp[-(y1-l1)/s1] + exp[-(y2-l2)/s2] )^3]
where s1>0 and s2>0 are the scale parameters, and l1 and l2 are the location parameters. Each of the two responses are unbounded, i.e., -Inf<y_j<Inf. The mean of Y1 is l1 etc. The fitted values are returned in a 2-column matrix. The cumulative distribution function is
F(y1,y2;l1,s1,l2,s2) = 1 / (1 + exp[-(y1-l1)/s1] + exp[-(y2-l2)/s2])
The marginal distribution of Y1 is
P(Y1 <= y1) = F(y1;l1,s1) = 1 / (1 + exp[-(y1-l1)/s1]).
By default, eta1=l1, eta2=log(s1), eta3=l2, eta4=log(s2) are the linear/additive predictors.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm and vgam.
T. W. Yee
Gumbel, E. J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association, 56, 335–349.
Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005). Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience.
## 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)
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