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#newton-raphson algo with p=1
NR1.ft=function(x,beta,psi.full,n,nt,Y,dN, maxiter,eps){
iter=0
dist=1
while(dist>=eps){
iter=iter+1
if(iter>maxiter) break
xb=x*beta
Yest=matrix(0,n,1)
U=H=0
for(i in 1:n){
for(j in which(dN[i,]>=1)){
Yest=Y[,j]*exp(psi.full+xb) #Y*estimated exp(psi.hat+xb)
S0=sum(Yest)
S1=sum(Yest*x)
S2=sum(Yest*x^2)
E1=S1/S0
U=U+(x[i]-E1)*dN[i,j]
H=H+(-S2/S0+E1^2)*dN[i,j]
}
}
beta.new = beta - U/H
#distance
dist=sqrt(sum((beta.new-beta)^2))
beta=beta.new
}
return(beta.new)
}
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