gammahyp {VGAM} | R Documentation |
Estimate the parameter of a gamma hyperbola bivariate distribution by maximum likelihood estimation.
gammahyp(ltheta="loge", itheta=NULL, expected=FALSE)
ltheta |
Link function applied to the (positive) parameter theta.
See Links for more choices.
|
itheta |
Initial value for the parameter.
The default is to estimate it internally.
|
expected |
Logical. FALSE means the Newton-Raphson (using
the observed information matrix) algorithm, otherwise the expected
information matrix is used (Fisher scoring algorithm).
|
The joint probability density function is given by
f(y1,y2) = exp( -exp(-theta) * y1 / theta - theta * y2)
for theta > 0, y1 > 0, y2 > 1. The random variables Y1 and Y2 are independent. The marginal distribution of Y1 is an exponential distribution with rate parameter exp(-theta)/theta. The marginal distribution of Y2 is an exponential distribution that has been shifted to the right by 1 and with rate parameter theta. The fitted values are stored in a two-column matrix with the marginal means, which are theta * exp(theta) and 1 + 1/theta.
The default algorithm is Newton-Raphson because Fisher scoring tends to be much slower for this distribution.
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.
T. W. Yee
Reid, N. (2003) Asymptotics and the theory of inference. Annals of Statistics, 31, 1695–1731.
x = runif(n <- 1000) theta = exp(-2+x) y1 = rexp(n, rate=exp(-theta)/theta) y2 = 1 + rexp(n, rate=theta) fit = vglm(cbind(y1,y2) ~ x, fam=gammahyp(expected=TRUE), trace=TRUE) fit = vglm(cbind(y1,y2) ~ x, fam=gammahyp, trace=TRUE, crit="coef") coef(fit, matrix=TRUE) Coef(fit) fitted(fit)[1:4,] summary(fit)