VGAM (version 0.7-3)

betageometric: Beta-geometric Distribution Family Function

Description

Maximum likelihood estimation for the beta-geometric distribution.

Usage

betageometric(lprob="logit", lshape="loge",
              eprob=list(), eshape=list(),
              iprob = NULL, ishape = 0.1,
              moreSummation=c(2,100), tolerance=1.0e-10, zero=NULL)

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 2-parameter beta-geometric distribution if $P(Y=y) = p (1-p)^y$ for $y=0,1,2,\ldots$ where $p$ are generated from a standard beta distribution with shape parameters shape1 and shape2. The parameterization here is to focus on the parameters $p$ and $\phi = 1/(shape1+shape2)$, where $\phi$ is shape. The default link functions for these ensure that the appropriate range of the parameters is maintained. The mean of $Y$ is $E(Y) = shape2 / (shape1-1) = (1-p) / (p-\phi)$.

The geometric distribution is a special case of the beta-geometric distribution with $\phi=0$ (see geometric). However, fitting data from a geometric distribution may result in numerical problems because the estimate of $\log(\phi)$ will 'converge' to -Inf.

References

Paul, S. R. (2005) Testing goodness of fit of the geometric distribution: an application to human fecundability data. Journal of Modern Applied Statistical Methods, 4, 425--433.

See Also

geometric, betaff, rbetageom.

Examples

y = 0:11; wts = c(227,123,72,42,21,31,11,14,6,4,7,28)
fit  = vglm(y ~ 1, fam=betageometric, weight=wts, trace=TRUE)
fitg = vglm(y ~ 1, fam=    geometric, weight=wts, trace=TRUE)
coef(fit, matrix=TRUE)
Coef(fit)
diag(vcov(fit, untrans=TRUE))^0.5
fit@misc$shape1
fit@misc$shape2
# Very strong evidence of a beta-geometric:
1-pchisq(2*(logLik(fit)-logLik(fitg)), df=1)