prentice74 {VGAM} | R Documentation |
Estimation of a 3-parameter log-gamma distribution described by Prentice (1974).
prentice74(llocation="identity", lscale="loge", lshape="identity", elocation=list(), escale=list(), eshape=list(), ilocation=NULL, iscale=NULL, ishape=NULL, zero=NULL)
llocation |
Parameter link function applied to the
location parameter a.
See Links for more choices.
|
lscale |
Parameter link function applied to the
positive scale parameter b.
See Links for more choices.
|
lshape |
Parameter link function applied to
the shape parameter q.
See Links for more choices.
|
elocation, escale, eshape |
List. Extra argument for each of the links.
See earg in Links for general information.
|
ilocation, iscale |
Initial value for a and b, respectively.
The defaults mean an initial value is determined internally for each.
|
ishape |
Initial value for q.
If failure to converge occurs, try some other value.
The default means an initial value is determined internally.
|
zero |
An integer-valued vector specifying which
linear/additive predictors are modelled as intercepts only.
The values must be from the set {1,2,3}.
The default value means none are modelled as intercept-only terms.
|
The probability density function is given by
f(y;a,b,q) = |q| * exp(w/q^2 - e^w) / (b*gamma(1/q^2)),
for shape parameter q != 0,
positive scale parameter b > 0,
location parameter a,
and all real y.
Here, w = (y-a)*q/b+psi(1/q^2)
where psi is the digamma function.
The mean of Y is a (returned as the fitted values).
This is a different parameterization compared to lgamma3ff
.
Special cases: q=0 is the normal distribution with standard deviation b, q=-1 is the extreme value distribution for maxima, q=1 is the extreme value distribution for minima (Weibull). If q>0 then the distribution is left skew, else q<0 is right skew.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
The special case q=0 is not handled, therefore estimates of q too close to zero may cause numerical problems.
The notation used here differs from Prentice (1974): alpha=a, sigma=b. Fisher scoring is used.
T. W. Yee
Prentice, R. L. (1974) A log gamma model and its maximum likelihood estimation. Biometrika, 61, 539–544.
x = runif(n <- 5000) loc = -1 + 2*x Scale = exp(1+x) y = rlgamma(n, loc=loc, scale=Scale, k=1) fit = vglm(y ~ x, prentice74(zero=3), trace=TRUE) coef(fit, matrix=TRUE) # Note the coefficients for location