library(aster)
ifam <- fam.truncated.poisson(truncation = 0)
mu <- seq(0.1, 3.0, 0.2)
theta <- log(mu)
zeroth <- double(length(theta))
first <- double(length(theta))
second <- double(length(theta))
for (i in seq(along = theta)) {
zeroth[i] <- famfun(ifam, 0, theta[i])
first[i] <- famfun(ifam, 1, theta[i])
second[i] <- famfun(ifam, 2, theta[i])
}
all.equal(zeroth, log(exp(mu) - 1))
tau <- mu / (1 - exp(- mu))
all.equal(first, tau)
all.equal(second, tau * (1 - tau * exp(- mu)))