residual.nr<-function(obs,hat,se){
cv =se/obs
sigma =(log(1+(cv)^2))^0.5
residual=log(obs/exp)/sigma
data.frame(cv=cv,
sigma=sigma,
residual=residual)}
residual.nr.ln<-function(obs,hat,bin,n){
p =n/sum(n)
mu.obs =sum(bin*obs)/sum(obs)
mu.hat =sum(bin*hat)/sum(hat)
n =mean(n)
sigma.nr =(sum(p*(bin-mu.obs)^2)/n)^0.5
residual =(mu.obs-mu.hat)/sigma.nr
residual.nr=residual/sigma.nr
data.frame(mu.obs =mu.obs,
mu.hat =mu.hat,
residual.nr=residual.nr,
sigma.nr =sigma.nr)}
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