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Topic: Monte Carlo simulation with inequality constraints
Replies: 11   Last Post: Mar 23, 2012 8:53 AM

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 deltaquattro@gmail.com Posts: 77 Registered: 7/21/06
Re: Monte Carlo simulation with inequality constraints
Posted: Mar 15, 2012 12:30 PM

Il giorno giovedì 15 marzo 2012 16:22:42 UTC+1, Dave Dodson ha scritto:
> Let R1, R2, R3, and R4 be four random numbers. Set X1 = max(R1,R2), X2 = min(R1,R2), X3 = max(R3,R4), and X4 = min(R3,R4).
>
> Dave

Cool, thanks! This sounds a bit like my solution 3, but using min and max instead than abs and + . In your case, which are the distribution of X1 and X2, for example? I guess they're different from the distributions of R1 and R2. Also, do you have any comment about solution 2, i.e.,

> > 2. I let the Monte Carlo code to generate freely the sample runs, and whenever a run has X1<X2 or X3<X4, I discard it. However, I'm worried that this "rejection process" may distort the distributions of the Xs. Also, I guess I'll need to perform four times as many Monte Carlo runs as usual, to have the same level of statistical convergence.

Do you know if in this case, the distributions of X1, X2, X3, X4 would be the same as without "rejection", or if they are different? Thanks,

Best Regards

deltaquattro

Date Subject Author
3/15/12 deltaquattro@gmail.com
3/15/12 Dave Dodson
3/15/12 deltaquattro@gmail.com
3/15/12 Ray Koopman
3/16/12 deltaquattro@gmail.com
3/16/12 Ray Koopman
3/19/12 deltaquattro@gmail.com
3/22/12 Ray Koopman
3/22/12 deltaquattro@gmail.com
3/22/12 Ray Koopman
3/23/12 deltaquattro@gmail.com
3/16/12 AMX