morgenstern {VGAM} | R Documentation |
Estimate the association parameter of Morgenstern's bivariate distribution by maximum likelihood estimation.
morgenstern(lapar="rhobit", earg=list(), iapar=NULL, tola0=0.01, method.init=1)
lapar |
Link function applied to the association parameter
alpha, which lies between -1 and 1.
See Links for more choices.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
iapar |
Numeric. Optional initial value for alpha.
By default, an initial value is chosen internally.
If a convergence failure occurs try assigning a different value.
Assigning a value will override the argument method.init .
|
tola0 |
Positive numeric.
If the estimate of alpha has an absolute
value less than this then it is replaced by this value.
This is an attempt to fix a numerical problem when the estimate
is too close to zero.
|
method.init |
An integer with value 1 or 2 which
specifies the initialization method. If failure to converge occurs
try the other value, or else specify a value for ia .
|
The cumulative distribution function is
P(Y1 <= y1, Y2 <= y2) = exp(-y1-y2) * ( 1 + alpha * [1 - exp(-y1)] * [1 - exp(-y2)] ) + 1 - exp(-y1) - exp(-y2)
for alpha between -1 and 1. The support of the function is for y1>0 and y2>0. The marginal distributions are an exponential distribution with unit mean. When alpha=0 then the random variables are independent, and this causes some problems in the estimation process since the distribution no longer depends on the parameter.
A variant of Newton-Raphson is used, which only seems to work for an
intercept model.
It is a very good idea to set trace=TRUE
.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
The response must be a two-column matrix. Currently, the fitted value is a matrix with two columns and values equal to 1. This is because each marginal distribution corresponds to a exponential distribution with unit mean.
This VGAM family function should be used with caution.
T. W. Yee
Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005) Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, N.J.: Wiley-Interscience.
n = 1000 ymat = cbind(rexp(n), rexp(n)) ## Not run: plot(ymat) fit = vglm(ymat ~ 1, fam=morgenstern, trace=TRUE) fit = vglm(ymat ~ 1, fam=morgenstern, trace=TRUE, crit="coef") coef(fit, matrix=TRUE) Coef(fit) fitted(fit)[1:5,]