alloc.n=function(data,g,Ni,s2i,cost,fcost,type,param,B){
  data=as.name(data); type=as.name(type); g=g; s2i=s2i
  stratname=levels(g); Ni=Ni; N=sum(Ni); si=sqrt(s2i)
  cost=cost; param=as.name(param); B=B; fcost=fcost
  if(param=='mean'){
    D=B^2/4
  } else if(param=='proportion'){
    D=B^2/4
  } else if(param=='total')
    D=B^2/(4*N^2)
  if(type=='optimal'){  
    ai=(Ni*si/sqrt(cost))/(sum(Ni*si/sqrt(cost)))
    n=ceiling((sum(Ni*si/sqrt(cost))*(sum(Ni*si*sqrt(cost))))/(N^2*D+sum(Ni*s2i)))
    ni=round(n*ai,0)
  }    else if(type=='fixed'){  
    ai=(Ni*si/sqrt(cost))/(sum(Ni*si/sqrt(cost)))
    n=floor(fcost/sum(cost*ai))
    ni=round(n*ai,0)
  }    else if(type=='Neyman'){
    ai=(Ni*si)/sum(Ni*si)
    n=ceiling((sum(Ni*si))^2/(N^2*D+sum(Ni*s2i)))
    ni=round(n*ai,0)
  }    else if(type=='proportional'){
    ai=Ni/N
    n=ceiling(sum(Ni*s2i)/(N*D+(1/N)*sum(Ni*s2i)))
    ni=round(n*ai,0)
  }
  cat('','\n','Results from StRS method: ',param,'\n','Data: ',data,'\n', 'Allocation method: '
      ,type,'\n', 'Population size =',N,'\n','Stratum =',stratname,'\n','Stratum sizes =',Ni,'\n',
      'Estimated variances =',s2i,'\n','Desired bound =',B,'\n','Allocation fractions (ai) =',
      ai,'\n','Estimated sample size =',n,'\n','Estimated stratum sample sizes =',ni,'\n','Note: there may be some discrepancies in sample sizes due to rounding errors','\n')
  results=list(type=type,data=data,N=N,Ni=Ni,stratname=stratname,ai=ai,param=param,n=n,ni=ni,B=B,fcost=fcost)
  
}

# to use the function with its call: alloc.n(data,g,Ni,s2i,cost,fcost,type,param,B)
# data: name of dataset, in quotes
# g: vector of stratum
# Ni: vector of population sizes
# s2i: vector of stratum variances (for proportions, s2i=pi*qi)
# cost: vector of stratum survey costs (if none, input a vector of 1s)
# fcost: (total) fixed cost (if none, use 1)
# type: c('optimal','fixed','Neyman','proportional')
# param: c('mean','total','proportion')
# B: desired bound