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ES.May<-function(mat,digs=3){
Nk<-apply(mat,1,sum)
i.names<-paste("i=",1:nrow(mat),sep="")
##calculate Pki matrix
Pk<-apply(mat,2,function(x){x/Nk})
rownames(Pk)<-rownames(mat)
colnames(Pk)<-i.names
##calculate N matrix
N.mat<-matrix(nrow=nrow(mat),ncol=nrow(mat))
for(i in 1:nrow(mat)){
N.mat[,i]<-rep((1/i),nrow(mat))*(Pk[,i]*Nk)}
rownames(N.mat)<-rownames(mat)
colnames(N.mat)<-i.names
##calculate fk vector
fk.mat<-matrix(nrow=nrow(mat),ncol=nrow(mat))
for(i in 1:nrow(mat)){
fk.mat[,i]<-rep((1/i),nrow(mat))*Pk[,i]}
fk.vec<-apply(fk.mat,1,sum)
names(fk.vec)<-rownames(mat)
rownames(fk.mat)<-rownames(mat)
colnames(fk.mat)<-i.names
##Nf
Nk.vec<-fk.vec*Nk
names(Nk.vec)<-rownames(mat)
res<-list()
res$E.S_coefficents<-cbind(N=sum(N.mat),F=sum(N.mat)/sum(Nk))
res$Nk<-Nk
res$Pki.matrix<-round(Pk,digs)
res$N.matrix<-round(N.mat,digs)
res$fk.matrix<-round(fk.mat, digs)
res$fk.vector<-round(fk.vec,digs)
res$Nk.vector<-round(Nk.vec,digs)
res
}
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