function mu_nr = EndPointCooke_rlargest(simData,r)

% Estimates the endpoint.
%
% see also EndPointSimulationCooke

simData = sort(simData);
%choose the r largest
rlargest = simData(end-r+1:end);
x1 = min(rlargest);
xn = max(rlargest);

v_nr = (1/(r-1)) * sum(log((xn-x1)./(xn-rlargest(2:end-1))));

row = repmat([1:r]',1,r);
col = row';

lambda = (gamma(2*v_nr + row).*gamma(v_nr + col)) ./ (gamma(v_nr+row).*gamma(col));
lambda = tril(lambda) + tril(lambda,-1)';

one = ones(r,1);
a = inv(one'*inv(lambda)*one) * inv(lambda) * one;

mu_nr = sum(a'.*fliplr(rlargest));