Random Draw from Inverse Gamma 1 Distribution

Estimation ML/Bayesian estimation
1

Dear friends,

Quick question: I am trying to write a code to generate random numbers from an Inverse Gamma (IG) distribution based on Dynare’s definition of an “Inverse Gamma 1 Distribution”. Under the “Wikipedia” version of IG, it is possible to get draws from an IG(a,b) from a Gamma(a,1/b), where “a” and “b” are the shape and scale parameters of the distribution. It is trivial to match these parameters with the “IG 2 Distribution”, but not with the “IG 1 Distribution”. Is there any quick fix to use the same structure of “IG 1” to generate random draws?

Thanks!

2

Have a look at

if inverse_gamma_1_draws
    pdraw(inverse_gamma_1_index) = ...
        sqrt(1./gamrnd(p7(inverse_gamma_1_index)/2,2./p6(inverse_gamma_1_index)))+p3(inverse_gamma_1_index);
    out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
    while ~isempty(out_of_bound)
        pdraw(inverse_gamma_1_index(out_of_bound)) = ...
            sqrt(1./gamrnd(p7(inverse_gamma_1_index(out_of_bound))/2,2./p6(inverse_gamma_1_index(out_of_bound))))+p3(inverse_gamma_1_index(out_of_bound));
        out_of_bound = find( (pdraw(inverse_gamma_1_index)'>ub(inverse_gamma_1_index)) | (pdraw(inverse_gamma_1_index)'<lb(inverse_gamma_1_index)));
    end
end

if inverse_gamma_2_draws
    pdraw(inverse_gamma_2_index) = ...
        1./gamrnd(p7(inverse_gamma_2_index)/2,2./p6(inverse_gamma_2_index))+p3(inverse_gamma_2_index);
    out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
    while ~isempty(out_of_bound)
        pdraw(inverse_gamma_2_index(out_of_bound)) = ...
            1./gamrnd(p7(inverse_gamma_2_index(out_of_bound))/2,2./p6(inverse_gamma_2_index(out_of_bound)))+p3(inverse_gamma_2_index(out_of_bound));
        out_of_bound = find( (pdraw(inverse_gamma_2_index)'>ub(inverse_gamma_2_index)) | (pdraw(inverse_gamma_2_index)'<lb(inverse_gamma_2_index)));
    end
end
3

Thank you so much. I will take a look at the code.

Best,

Angelo