Nothing
fitting <- function(degree.dist,nmax){
n.regions<-length(degree.dist)
tmp<-hist(degree.dist,breaks=c(0:nmax))
cum.dist<-1-cumsum(tmp$counts)/n.regions # cumulative distribution of degree.dist
mu<-1/(sum(degree.dist)/n.regions) # parameter of the exponential law
nb<-length(degree.dist[degree.dist>0])
gamma<-1+nb/(sum(log(degree.dist[degree.dist>0]))) # parameter of the power law
x<-degree.dist
x<-x[x>0]
n<-length(x)
fn<-function(p) -(-n*p*log(sum(x)/(n*p))-n*log(gamma(p))+(p-1)*sum(log(x))-n*p)
# - log likelihood for the truncated power law with only one parameter
out <- nlm(fn, p = 1, hessian = TRUE) # Minimisation of fn
alpha<-out$estimate
beta<-sum(degree.dist)/(n.regions*alpha)
# parameters of the truncated power law
# Computation of AIC
AIC.exp<--2*(n.regions*log(mu)-mu*sum(degree.dist))+2
AIC.pow<--2*(n.regions*log(gamma-1)-gamma*sum(log(x)))+2
AIC.trunc<--2*(-out$minimum)+2
fitting<-"mu ="
fitting<-paste(fitting,mu,sep=" ")
fitting<-paste(fitting,"gamma = ",sep="\n")
fitting<-paste(fitting,gamma,sep=" ")
fitting<-paste(fitting,"alpha = ",sep="\n")
fitting<-paste(fitting,alpha,sep=" ")
fitting<-paste(fitting,"beta = ",sep="\n")
fitting<-paste(fitting,beta,sep=" ")
fitting<-paste(fitting,"AIC exp = ",sep="\n")
fitting<-paste(fitting,AIC.exp,sep=" ")
fitting<-paste(fitting,"AIC pow = ",sep="\n")
fitting<-paste(fitting,AIC.pow,sep=" ")
fitting<-paste(fitting,"AIC trunc = ",sep="\n")
fitting<-paste(fitting,AIC.trunc,sep=" ")
# file with all the value of the fittings
write.table(fitting,"fitting.txt",row.names=FALSE,col.names=FALSE,quote=FALSE)
list(mu = mu, gamma = gamma, alpha = alpha, beta = beta)
}
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