Comparison the two ratios

glm_pois.R

n <- 1000
rate <- 1
set.seed(1234)
tau_x <- rgamma(n,1,1)
X <- rpois(n,tau_x*rate)
tau_y <- rgamma(n,2,1)
Y <- rpois(n,tau_y*rate)
#png("ECDF_rate.png")
curve(ecdf(X/tau_x)(x), type = "s", xlim = c(0, 15), ylim=c(0,1), col="royalblue", ylab = "ECDF", xlab = "ratio")
curve(ecdf(Y/tau_y)(x), type = "s", add=TRUE, col="orangered", lty=2)
#dev.off()
print(wilcox.test(X/tau_x,Y/tau_y))

target <- c(X,Y)
predictor <- rep(c(0,1),each=n)
logtau <- log(c(tau_x,tau_y))
fit <- glm(target ~ predictor+offset(logtau), family = poisson(link = "log"))
print(summary(fit))