NTypes = 400;
nums = 1:NTypes;
D = (1./(1:NTypes)).^1.6;
PD = D/sum(D);
HD = -sum(PD.*log(PD));
%
NN=100000;
ND = round(NN*PD);
C = zeros(NN,1);
loc=1;
for n=1:NTypes
    for m=1:ND(n)
        C(loc)=n; loc = loc+1;
    end
end
CC = C(randperm(NN));
CCm = CC(1:(NN-1));  % to avoid running off the end
HLL = zeros(NTypes,1);
Sizes = zeros(NTypes,1);
for n=2:NTypes
   D=histc(CC(find(CCm<=n)),nums);
   DD=D(D>0);
   Sizes(n) = length(DD);
   PD=DD/sum(DD);
   HLL(n)= -sum(PD.*log(PD));
end
HLLn = HLL(20:20:NTypes);
%
plot(20:20:NTypes,HLLn,'-or')
ylim([0 6]); 
ylabel('Conditional Entropy');
xlabel('Number of Tokens');