%sample from the prior distribution..
%this uses different priors. l1 and l2 uniform. Alpha is gamma



%want to sample KK values from prior distribution
%lambda1 +lamda2 =prior_l = max failure rate 
%priors for lamdas are appropiate uniforms.
%Assume alpha is gamma(0,b,a) - location 0, scale b, shape a.

for k=1:KK
    
    samples(k,1)=prior_l;
    samples(k,2)= samples(k,1);
    while (samples(k,1)+samples(k,2))>prior_l
        u(1:2) = rand(1,2);  %generate 2 random numbers between 0,1 from uniform, each corresponding to different parameters
        samples(k,1) = prior_l-prior_l*((1-u(1))^.5);  
        samples(k,2) = prior_l-prior_l*((1-u(2))^.5);
    end
end
samples(:,3) = randraw('gamma',[0 (prior_var_al/prior_x_al) (((prior_x_al)^2)/prior_var_al)],KK);
clear u k