VGAM (version 0.8-2)

geometric: Geometric Distribution

Description

Maximum likelihood estimation for the geometric distribution.

Usage

geometric(link = "logit", earg=list(), expected = TRUE, method.init = 1)

Arguments

link

Parameter link function applied to the parameter $p$, 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.

Value

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

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).

References

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

See Also

negbinomial, Geometric, betageometric, expgeometric, 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, mat=TRUE)
summary(fit)