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Bug fix. This version can be used in the estimated_params block. 

git-svn-id: https://www.dynare.org/svn/dynare/trunk@2538 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
stepan 2009-03-28 22:43:38 +00:00
parent 4bbf29ac1b
commit ec4cc46845
1 changed files with 49 additions and 59 deletions
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108
matlab/distributions/mode_and_variance_to_mean.m
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@ -4,17 +4,18 @@ function [mu, parameters] = mode_and_variance_to_mean(m,s2,distribution,lower_bo
% INPUTS
% m [double] scalar, mode of the distribution.
% s2 [double] scalar, variance of the distribution.
% distribution [string] name of the distribution ("gamma","inv-gamma-2","inv-gamma-1","beta")
% distribution [integer] scalar for the distribution shape
% 1 gamma
% 2 inv-gamma-2
% 3 inv-gamma-1
% 4 beta
% lower_bound [double] scalar, lower bound of the random variable support (optional).
% upper_bound [double] scalar, upper bound of the random variable support (optional).
%
% OUTPUT
% mu [double] scalar, mean of the distribution.
% parameters [double] 2*1 vector, parameters of the distribution.
% info [integer] scalar. If info=1 we have a multiplicity of solutions.
% If info=2 we have no solution.
% ALGORITHM
% Described in "Prior Distribution in Dynare".
%
% Copyright (C) 2009 Dynare Team
%
@ -34,82 +35,72 @@ function [mu, parameters] = mode_and_variance_to_mean(m,s2,distribution,lower_bo
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
% Check input aruments.
if ~(nargin==3 || nargin==5 || nargin==4)
if ~(nargin==3 || nargin==5 || nargin==4 )
error('mode_and_variance_to mean:: 3 or 5 input arguments are needed!')
end
if ~ischar(distribution)
error(['mode_and_variance_to_mean:: Third argument must be a string!'])
end
% Set defaults bounds.
if nargin==3
switch distribution
case 'gamma'
case 1
lower_bound = 0;
upper_bound = Inf;
case 'inv-gamma-1'
case 3
lower_bound = 0;
upper_bound = Inf;
case 'inv-gamma-2'
case 2
lower_bound = 0;
upper_bound = Inf;
case 'beta'
case 4
lower_bound = 0;
upper_bound = 1;
otherwise
disp(['mode_and_variance_to mean:: ' distribution ' is an unknown distribution...'])
disp(' distribution is equal to ''beta'', ''gamma'',')
disp(' ''inv-gamma-1'' or ''inv-gamma-2'' ')
error()
error('Unknown distribution!')
end
end
if nargin==4
switch distribution
case 'gamma'
case 1
upper_bound = Inf;
case 'inv-gamma-1'
case 3
upper_bound = Inf;
case 'inv-gamma-2'
case 2
upper_bound = Inf;
case 'beta'
case 4
upper_bound = 1;
otherwise
disp(['mode_and_variance_to mean:: ' distribution ' is an unknown distribution...'])
disp(' distribution is equal to ''beta'', ''gamma'',')
disp(' ''inv-gamma-1'' or ''inv-gamma-2'' ')
error()
error('Unknown distribution!')
end
end
if strcmpi(distribution,'gamma')
if (distribution==1)% Gamma distribution
if m<lower_bound
error('mode_and_variance_to_mean:: The mode has to be greater than the lower bound!')
error('The mode has to be greater than the lower bound!')
end
if (m-lower_bound)<1e-12
error('mode_and_variance_to_mean:: The gamma distribution should be specified with the mean and variance.')
error('The gamma distribution should be specified with the mean and variance.')
end
m = m - lower_bound ;
tmp = 1-sqrt(4*s2/(m*m));
alpha = 1 - 2/tmp;
beta = -.5*m*tmp;
beta = -.5*m*(1-sqrt(1+4*s2/(m*m))) ;
alpha = (m+beta)/beta ;
parameters(1) = alpha;
parameters(2) = beta;
mu = alpha*beta + lower_bound ;
return
end
if strcmpi(distribution,'inv-gamma-2')
if (distribution==2)% Inverse Gamma - 2 distribution
if m<lower_bound+2*eps
error('mode_and_variance_to_mean:: The mode has to be greater than the lower bound!')
error('The mode has to be greater than the lower bound!')
end
m = m - lower_bound ;
if isinf(s2)
nu = 2;
s = 4*m;
nu = 4;
s = 2*m;
else
delta = 2*m*m/s2;
poly = [ 1 , -6 , 12-delta , -8-2*delta ];
delta = 2*(m*m/s2);
poly = [ 1 , -(8+delta) , 20-4*delta , -(16+4*delta) ];
all_roots = roots(poly);
real_roots = all_roots(find(abs(imag(all_roots))<2*eps));
nu = real_roots(find(real_roots>2));
@ -121,23 +112,22 @@ function [mu, parameters] = mode_and_variance_to_mean(m,s2,distribution,lower_bo
return
end
if strcmpi(distribution,'inv-gamma-1')
if (distribution==3)% Inverted Gamma 1 distribution
if m<lower_bound+2*eps
error('mode_and_variance_to_mean:: The mode has to be greater than the lower bound!')
error('The mode has to be greater than the lower bound!')
end
m = m - lower_bound ;
if isinf(s2)
nu = 2;
s = 1/(m*m);
else
[mu, parameters] = mode_and_variance_to_mean(m,s2,'inv-gamma-2');
[mu, parameters] = mode_and_variance_to_mean(m,s2,2);
nu = sqrt(parameters(1));
nu2 = 2*nu;
nu1 = 2;
tmp = s2*m*m;
err = tmp - (nu-1)/(nu-2) + .5*(nu-1)*(gamma((nu-1)/2)/gamma(nu/2))^2;
err = s2*(m*m) - (nu-1)/(nu-2) + .5*(nu-1)*(gamma((nu-1)/2)/gamma(nu/2))^2;
while abs(nu2-nu1) > 1e-12
if err > 0
if err < 0
nu1 = nu;
if nu < nu2
nu = nu2;
@ -149,9 +139,9 @@ function [mu, parameters] = mode_and_variance_to_mean(m,s2,distribution,lower_bo
nu2 = nu;
end
nu = (nu1+nu2)/2;
err = tmp - (nu-1)/(nu-2) + .5*(nu-1)*(gamma((nu-1)/2)/gamma(nu/2))^2;
err = s2*(m*m) - (nu-1)/(nu-2) + .5*(nu-1)*(gamma((nu-1)/2)/gamma(nu/2))^2;
end
s = (nu-1)/m^2 ;
s = (nu-1)/(m*m) ;
end
parameters(1) = nu;
parameters(2) = s;
@ -159,35 +149,35 @@ function [mu, parameters] = mode_and_variance_to_mean(m,s2,distribution,lower_bo
return
end
if strcmpi(distribution,'beta')
if (distribution==4)% Beta distribution
if m<lower_bound
error('mode_and_variance_to_mean:: The mode has to be greater than the lower bound!')
error('The mode has to be greater than the lower bound!')
end
if m>upper_bound
error('mode_and_variance_to_mean:: The mode has to be less than the upper bound!')
error('The mode has to be less than the upper bound!')
end
if (m-lower_bound)<1e-12
error('mode_and_variance_to_mean:: The beta distribution should be specified with the mean and variance.')
error('The beta distribution should be specified with the mean and variance.')
end
if (upper_bound-m)<1e-12
error('mode_and_variance_to_mean:: The beta distribution should be specified with the mean and variance.')
error('The beta distribution should be specified with the mean and variance.')
end
ll = upper_bound-lower_bound;
m = (m-lower_bound)/ll ;
s2 = s2/(ll*ll) ;
m = (m-lower_bound)/ll;
s2 = s2/(ll*ll);
delta = m^2/s2;
poly = NaN(1,4);
poly(1) = 1/m^3;
poly(2) = (7*m*s2-3*s2+m^3-m^2)/(m^3*s2);
poly(3) = (16*m^2*s2-14*m*s2+3*s2-2*m^3+m^2)/(m^3*s2);
poly(4) = 12*m^3-16*m^2-7*m-1;
poly(1) = 1;
poly(2) = 7*m-(1-m)*delta-3;
poly(3) = 16*m^2-14*m+3-2*m*delta+delta;
poly(4) = 12*m^3-16*m^2+7*m-1;
all_roots = roots(poly);
real_roots = all_roots(find(abs(imag(all_roots))<2*eps));
idx = find(real_roots>1);
if length(idx)>1
error('mode_and_variance_to_mean:: Multiplicity of solutions for the beta distribution specification.')
error('Multiplicity of solutions for the beta distribution specification.')
elseif isempty(idx)
disp('mode_and_variance_to_mean:: No solution for the beta distribution specification.')
disp(' You should reduce the variance.');
disp('No solution for the beta distribution specification. You should reduce the variance.')
error();
end
alpha = real_roots(idx);