geometric {VGAM}R Documentation

Geometric Distribution

Description

Maximum likelihood estimation for the geometric distribution.

Usage

geometric(link = "logit", earg=list(), expected = TRUE, imethod = 1)

Arguments

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.

imethod

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.

Details

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).

Value

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

Author(s)

T. W. Yee

References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

See Also

negbinomial, Geometric, betageometric, expgeometric, zigeometric, rbetageom.

Examples

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, matrix = TRUE)
summary(fit)
[Package VGAM version 0.8-4 Index]