fgm {VGAM} | R Documentation |
Estimate the association parameter of Farlie-Gumbel-Morgenstern's bivariate distribution by maximum likelihood estimation.
fgm(lapar="rhobit", earg=list(), iapar=NULL, imethod=1, nsimEIM=200)
lapar |
Link function applied to the association parameter
alpha, which is real.
See |
earg |
List. Extra argument for the link.
See |
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 |
imethod |
An integer with value |
nsimEIM |
See |
The cumulative distribution function is
P(Y1 <= y1, Y2 <= y2) = y1 * y2 * ( 1 + alpha * (1 - y1) * (1 - y2) )
for -1 < alpha < 1. The support of the function is the unit square. The marginal distributions are the standard uniform distributions. When alpha=0 the random variables are independent.
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 0.5. This is because each marginal distribution corresponds to a standard uniform distribution.
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.
rfgm
,
frank
,
morgenstern
.
ymat = rfgm(n = 1000, alpha=rhobit(3, inverse=TRUE)) ## Not run: plot(ymat, col="blue") fit = vglm(ymat ~ 1, fam=fgm, trace=TRUE) coef(fit, matrix=TRUE) Coef(fit) head(fitted(fit))