geometric {VGAM} | R Documentation |
Maximum likelihood estimation for the geometric distribution.
geometric(link = "logit", earg=list(), expected = TRUE, method.init = 1)
link |
Parameter link function applied to the
parameter prob, which lies in the unit interval.
See Links for more choices.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
expected |
Logical.
Fisher scoring is used if expected = TRUE , else Newton-Raphson.
|
method.init |
An integer with value 1 or 2 or 3 which
specifies the initialization method for the probability.
If failure to converge occurs try another value.
|
A random variable Y has a 1-parameter geometric distribution
if P(Y=y) = prob * (1-prob)^y
for y=0,1,2,....
Here, prob is the probability of success,
and Y is the number of (independent) trials that are fails
until a success occurs.
Thus the response Y should be a non-negative integer.
The mean of Y is E(Y) = (1-prob)/prob
and its variance is Var(Y) = (1-prob)/prob^2.
The geometric distribution is a special case of the
negative binomial distribution (see negbinomial
).
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
negbinomial
,
Geometric
,
betageometric
,
rbetageom
.
gdata = data.frame(x2 = runif(nn <- 1000) - 0.5) gdata = transform(gdata, x3 = runif(nn) - 0.5, x4 = runif(nn) - 0.5) gdata = transform(gdata, eta = 1.0 - 1.0 * x2 + 2.0 * x3) gdata = transform(gdata, prob = logit(eta, inverse=TRUE)) gdata = transform(gdata, y = rgeom(nn, prob)) with(gdata, table(y)) fit = vglm(y ~ x2 + x3 + x4, geometric, gdata, trace=TRUE) coef(fit, mat=TRUE) summary(fit)