geometric {VGAM}R Documentation

Geometric Distribution

Description

Maximum likelihood estimation for the geometric distribution.

Usage

geometric(link = "logit", expected = TRUE)

Arguments

link Parameter link function applied to the parameter prob, which lies in the unit interval. See Links for more choices.
expected Logical. Fisher scoring is used if expected = TRUE, else Newton-Raphson.

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, rbetageom.

Examples

x1 = runif(n <- 1000) - 0.5
x2 = runif(n) - 0.5
x3 = runif(n) - 0.5
eta = 0.2 - 0.7 * x1 + 1.9 * x2
prob = logit(eta, inverse=TRUE)
y = rgeom(n, prob)
table(y)
fit = vglm(y ~ x1 + x2 + x3, geometric, trace=TRUE, crit="coef")
coef(fit)
coef(fit, mat=TRUE)
summary(fit)

[Package VGAM version 0.7-1 Index]