posbinomial {VGAM} | R Documentation |
Fits a positive binomial distribution.
posbinomial(link = "logit", earg=list())
link |
Link function for the usual probability parameter.
See Links for more choices.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
The positive binomial distribution is the ordinary binomial distribution but with the probability of zero being zero. Thus the other probabilities are scaled up (i.e., divided by 1-P(Y=0)).
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
rrvglm
and vgam
.
Under- or over-flow may occur if the data is ill-conditioned.
The input for this family function is the same as
binomialff
.
Yet to be done: a quasi.posbinomial
which estimates a dispersion
parameter.
Thomas W. Yee
Patil, G. P. (1962) Maximum likelihood estimation for generalised power series distributions and its application to a truncated binomial distribution. Biometrika, 49, 227–237.
Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.
# Number of albinotic children in families with 5 children # Data from Patil (1962) y = c(rep(1,25), rep(2,23), rep(3,10), 4, 5) # No zeros n = rep(5, 60) yprop = y / 5 # Fit the identical models in two ways; MLE of p is 0.3088 fit = vglm(yprop ~ 1, posbinomial, trace=TRUE, weights=n) fit2 = vglm(cbind(y, n-y) ~ 1, posbinomial, trace=TRUE) summary(fit) summary(fit2) Coef(fit2) # = MLE of p Coef(fit) # = MLE of p fitted(fit2)[1:2] fitted(fit)[1:2]