function bounds = tauboundaries(family);
%
%   FUNCTION BOUNDS, FUNC = TAUBOUNDARIES(FAMILY)
%
%   Return the minimum and maximum Kendall's tau spanned by a given copula
%   family.
% 
%   INPUT
%       FAMILY: One from {'AMH' 'Arch12' 'Arch14' 'Clayton' 'FGM' 'Frank'
%               'Gaussian' 'Gumbel' 't'}
%
%   OUTPUT
%       BOUNDS: [tau_min, tau_max]
%               Domain spanned by Kendall's tau for FAMILY.
%

%   D. Huard, Nov. 2006

tau_min = -1;
tau_max = 1;
switch lower(family)    
    case 'amh'
        tau_min = -0.181726;
        tau_max = 1/3;    
    case {'arch12' 'arch14'}
        tau_min = 1/3;
    case 'clayton' 
        tau_min = eps;
    case 'fgm'
        tau_min = -2/9;
        tau_max = 2/9;    
    case 'frank'
        % Discontinuity at 0
        tau_min = -1;
        tau_max = 1;
    case {'gaussian' 't'}        
    case 'gumbel'
        tau_min = 0.;
    otherwise 
        error('Copula family ''%s'' not recognized.', family)
end

bounds =  [tau_min, tau_max];