MATLAB: Loop to pick random variables from separate probability distributions

probability beta random

I have a dataset that can be described by a beta probability distribution (alpha = 3.18, beta = 44.87). What I want to do is pick a random value from that beta probability distribution, and depending how many standard deviations away from the mean that value is, I would like to select a second random value from a lognormal distrbution (mu=45.89, sigma=151.595) that is also within the specific standard deviation range.
Summarized: if a value of 0.17 is picked from my beta distrbution (which lies to the right of the mean and is greater than 2nd std, but less than the 3rd std) then I want to pick a random value from my lognormal distrbution that is also to the right of the mean and greater than the 2nd std but less than the 3rd std).
Firstly, I apologize as I am very new to this (1 week in). But the main issue with my code is that I do not properly know how to pick a random value from my lognormal distrbution within a specific standard deviation range. In the below code I have this step simply as the placeholder: Perm = lognrnd(45.89,151.5956,[1 1]). I am also missing one line of code at the end of my for loop which would copy my porRandom value into one column and Perm into a second column after each of the 300 runs, resulting in a 300×2 matrix.
Thanks for taking the time!
number_of_runs = 300;                                                                                  % Run this loop 300 times
porRandom = betarnd(3.1800,44.87,[1 1]);                                                               % porRandom = random number generated from a beta distribution within a 1x1 matrix
Perm = (number_of_runs,1);                                                                             % Generate a value for perm for each loop
for n = 1:number_of_runs;                                                                   
if porRandom <= (mean(porDist) + std(porDist)) OR >= (mean(porDist) - std(porDist));                   % if porRandom is within one standard deviation of the mean of a beta distrbution (porDist)
    Perm = lognrnd(45.89,151.5956,[1 1])                                                               % then let Perm be equal to a random value within one standard deviation of a defined lognormal distrbution
else if porRandom < (mean(porDist) - (std(porDist) AND > (mean(porDist) - ((std(porDist))*2));         % else if porRandom is within a 1st to 2nd standard deviation range (less than the mean)
        Perm = lognrnd(45.89,151.5956,[1 1])                                                           % then let Perm be equal to a random value within a 1st to 2nd standard deviation range (less than the mean) of a defined lognormal distrbution
    else if porRandom < (mean(porDist) - (((std(porDist))*2))                                          % else if porRandom is greater than 2 standard deviations (less than the mean)
            Perm = lognrnd(45.89,151.5956,[1 1]                                                        % then let Perm be equal to a random value that is greater than 2 standard deviations (less than the mean)
        else if porRandom > (mean(porDist) + (std(porDist) AND < (mean(porDist) + ((std(porDist))*2)); % else if porRandom is within a 1st to 2nd standard deviation range (greater than the mean)
                Perm = lognrnd(45.89,151.5956,[1 1]                                                    % then let Perm be equal to a random value within a 1st to 2nd standard deviation range (greater than the mean) of a defined lognormal distrbution 
            else porRandom > (mean(porDist) + (((std(porDist))*2));                                    % else porRandom is greater than two standard deviations (greater than the mean)
                    Perm = lognrnd(45.89,151.5956,[1 1]                                                % then let Perm be equal to a random value that is greater than 2 standard deviations (greater than the mean) 
end

Best Answer

It sounds like you want to select the second number from a truncated version of the lognormal distribution. If I understand what you are after, here is one way to do it with Cupid (just generating one random number for an example):
% Set up the beta distribution
% dist1 = Beta(3.18,44.87);
dist1.PlotDens   % Make sure this is the distribution you want

dist1sd = dist1.SD
% Set up the lognormal
% dist2 = LognormalMS(45.89,151.595);
dist2.PlotDens  % Make sure this is the distribution you want
dist2mn = dist2.Mean
dist2sd = dist2.SD
% Generate a random beta and find out where it lies in terms of SD's
dist1rnd = 0.17;  % or dist1rnd = dist1.Random to pick this randomly
dist1lowsd = floor( (dist1rnd-dist1.Mean) / dist1sd )
dist1hisd = ceil( (dist1rnd-dist1.Mean) / dist1sd )
% Bound the lognormal to lie within the same range of sds.
boundedlognormal = TruncatedX(dist2,dist2mn+dist1lowsd*dist2sd,dist2mn+dist1hisd*dist2sd);
desiredrandom = boundedlognormal.Random   % Get a random lognormal from that restricted range
desiredrandomsd = (desiredrandom - dist2mn) / dist2sd  % Check: Should be between dist1lowsd & dist1hisd
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