# geometric

0th

Percentile

##### Geometric (Truncated and Untruncated) Distributions

Maximum likelihood estimation for the geometric and truncated geometric distributions.

Keywords
models, regression
##### Usage
geometric(link = "logitlink", expected = TRUE, imethod = 1,
iprob = NULL, zero = NULL)
truncgeometric(upper.limit = Inf,
iprob = NULL, zero = NULL)
##### Arguments

Parameter link function applied to the probability parameter $$p$$, which lies in the unit interval. See Links for more choices.

expected

Logical. Fisher scoring is used if expected = TRUE, else Newton-Raphson.

iprob, imethod, zero

See CommonVGAMffArguments for details.

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.

##### Details

A random variable $$Y$$ has a 1-parameter geometric distribution if $$P(Y=y) = p (1-p)^y$$ for $$y=0,1,2,\ldots$$. Here, $$p$$ 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 $$E(Y) = (1-p)/p$$ and its variance is $$Var(Y) = (1-p)/p^2$$. 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 $$p$$ 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.

##### Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

##### References

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011) Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

negbinomial, Geometric, betageometric, expgeometric, zageometric, zigeometric, rbetageom, simulate.vlm.

##### Aliases
• geometric
• truncgeometric
##### Examples
# NOT RUN {
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)
# }

Documentation reproduced from package VGAM, version 1.1-1, License: GPL-3

### Community examples

Looks like there are no examples yet.