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How can I use covariance in random number generation
of a normal distribution? For example, I would use VBA to implement Box-Mueller using mean and std dev. I have implemented B-M in C. Can someone provide an algorithm (VBA, C or pseudocode) that incorporates covariance between two and among 3 or more random variables, each normally distributed? Is that called multivariate normal random number generation? FYI, This is for Monte Carlo simulation, if that matters. And I would be content with (even prefer) an algorithm that depends on a uniform RNG. Also, can I accomplish this without using VBA? For example, some people have suggested using NORMDIST(RAND(),mean,sd) as an RNG with normal distribution based on mean and std dev. I don't know how good that is and how that compares quality-wise to Box-Mueller, even assuming that RAND() is a good uniform RNG. (I believe some people question that assumption.) Frankly, I don't know how good Box-Mueller is quality-wise either, assuming a good uniform RNG to start with. I believe some people quibble over B-M as well. But I prefer to keep the discussion simple for now. I am interested in fundamental algorithms, not quibbles about perfection. |
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