MATLAB: How to generate Conditional Lognormal distribution

multivariate lognormal conditional distribution

Hi Community,
I am trying to create the 10000 sets of random variates of two parameters (a and b) from lognormal distribution with a condition that exp((b-a)/a)*1000 < 5;
a –> mu_a = 0.06, sigma_a = 50;
b –> mu_b = 0.08, sigma_b = 35;
I get to know from documentation for one variable as below but not sure about two varible that follow above condition.
pd = makedist('Lognormal','mu',0.08,'sigma',35);
t = truncate(pd, 0, inf);
r = random(t,10000,1);
Any help would be much appreciated. Thanks in advance.

Best Answer

Those mu and sigma values don't look right for lognormal distributions. These distributions have only positive values, so they have to be really wildly skewed to have such small means with such large standard deviations. Also, the cutoff of 5 looks too small for these parameters, because a and b will virtually never give a result satisfying the condition. But I think that something like this would work if you adjust the parameters:
mu_a = 0.06; sigma_a = 0.50;
mu_b = 0.08; sigma_b = 0.35;
cutoff = 1020;
nWanted = 10000;
nBatch = 1000;
storedA = [];
storedB = [];
while length(storedA) < nWanted
    a = lognrnd(mu_a,sigma_a,nBatch,1);
    b = lognrnd(mu_b,sigma_b,nBatch,1);
    y = exp((b-a)./a)*1000;
    keep = y < cutoff;
    storedA = [storedA; a(keep)];
    storedB = [storedB; b(keep)];
    mean(keep)
end
storedA = storedA(1:nWanted);
storedB = storedB(1:nWanted);
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