# How can I generate Conditional Lognormal distribution

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Vijay on 13 Jul 2020
Commented: Vijay on 14 Jul 2020
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.

Jeff Miller on 14 Jul 2020
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);
Vijay on 14 Jul 2020
Thanks Jeff. I realized that the sigma values are too small and corrected to the literature values.
It works.