Geometric (Truncated and Untruncated) Distributions
Maximum likelihood estimation for the geometric and truncated geometric distributions.
geometric(link = "logitlink", expected = TRUE, imethod = 1,
iprob = NULL, zero = NULL)
truncgeometric(upper.limit = Inf,
link = "logitlink", expected = TRUE, imethod = 1,
iprob = NULL, zero = NULL)link |
Parameter link function applied to the
probability parameter prob, which lies in the unit interval.
See |
expected |
Logical.
Fisher scoring is used if |
iprob, imethod, zero |
See |
upper.limit |
Numeric. Upper values. As a vector, it is recycled across responses first. The default value means both family functions should give the same result. |
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).
The geometric distribution is also a special case of the
Borel distribution, which is a Lagrangian distribution.
If Y has a geometric distribution with parameter prob then
Y+1 has a positive-geometric distribution with the same parameter.
Multiple responses are permitted.
For truncgeometric(),
the (upper) truncated geometric distribution can have response integer
values from 0 to upper.limit.
It has density prob * (1 - prob)^y / [1-(1-prob)^(1+upper.limit)].
For a generalized truncated geometric distribution with integer values L to U, say, subtract L from the response and feed in U-L as the upper limit.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
T. W. Yee. Help from Viet Hoang Quoc is gratefully acknowledged.
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
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 = logitlink(eta, inverse = TRUE))
gdata <- transform(gdata, y1 = rgeom(nn, prob))
with(gdata, table(y1))
fit1 <- vglm(y1 ~ x2 + x3 + x4, geometric, data = gdata, trace = TRUE)
coef(fit1, matrix = TRUE)
summary(fit1)
# Truncated geometric (between 0 and upper.limit)
upper.limit <- 5
tdata <- subset(gdata, y1 <= upper.limit)
nrow(tdata) # Less than nn
fit2 <- vglm(y1 ~ x2 + x3 + x4, truncgeometric(upper.limit),
data = tdata, trace = TRUE)
coef(fit2, matrix = TRUE)
# Generalized truncated geometric (between lower.limit and upper.limit)
lower.limit <- 1
upper.limit <- 8
gtdata <- subset(gdata, lower.limit <= y1 & y1 <= upper.limit)
with(gtdata, table(y1))
nrow(gtdata) # Less than nn
fit3 <- vglm(y1 - lower.limit ~ x2 + x3 + x4,
truncgeometric(upper.limit - lower.limit),
data = gtdata, trace = TRUE)
coef(fit3, matrix = TRUE)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.