MarshallEb: Marshall's global method-of-moments empirical-Bayes
rates (Poisson or binomial), as spdep::EBest (Poisson-gamma
empirical Bayes is PoissonGammaEb).
PotthoffWhittinghill: \(T = E_+ \sum O_i (O_i - 1) / E_i\) with
asymptotic mean \(O_+ (O_+ - 1)\) and variance
\(2 (k - 1) O_+ (O_+ - 1)\), as DCluster::pottwhitt.stat.
Identical to the Python arm morie.fn.smallarea.
Usage
MarshallEb(cases, population, family = "poisson")
PotthoffWhittinghill(observed, expected)
Arguments
- cases, population
Case counts and populations at risk.
- family
"poisson" or "binomial".
- observed, expected
Observed and expected counts.
References
Marshall, R. J. (1991). Mapping disease and mortality rates
using empirical Bayes estimators. Applied Statistics 40, 283-294.
Potthoff, R. F. and Whittinghill, M. (1966). Testing for homogeneity:
II. The Poisson distribution. Biometrika 53, 183-190.
Examples
MarshallEb(c(2, 8), c(100, 100))$estimate
#> [1] 0.03666667 0.06333333
PotthoffWhittinghill(c(3, 3, 3, 3), rep(3, 4))$T
#> [1] 96
