BayesGOF (version 4.0)

gMLE.pg: Negative-Binomial Parameter Estimation

Description

Computes Type-II Maximum likelihood estimates \(\hat{\alpha}\) and \(\hat{\beta}\) for gamma prior \(g\sim\) Gamma\((\alpha, \beta)\).

Usage

gMLE.pg(cnt.vec, exposure = NULL, start.par = c(1,1))

Arguments

cnt.vec

Vector containing Poisson counts.

exposure

Vector containing exposures for each count. The default is no exposure, thus exposure = NULL.

start.par

Initial values that will pass to optim.

Value

Returns a vector where the first component is \(\alpha\) and the second component is the scale parameter \(\beta\) for the gamma distribution: \(\frac{1}{\Gamma(\alpha)\beta^\alpha} \theta^{\alpha-1}e^{-\frac{\theta}{\beta}}.\)

References

Koenker, R. and Gu, J., 2017. "REBayes: An R Package for Empirical Bayes Mixture Methods," Journal of Statistical Software, Articles, 82(8), pp. 1-26.

Examples

# NOT RUN {
### without exposure
data(ChildIll)
ill.start <- gMLE.pg(ChildIll)
ill.start
### with exposure
data(NorbergIns)
X <- NorbergIns$deaths
E <- NorbergIns$exposure/344
norb.start <- gMLE.pg(X, exposure = E)
norb.start
# }