# Conditional Normal Random Distribution

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Vinit Nagda on 19 Aug 2021
Commented: Paul on 23 Aug 2021
I want to generate a random vector (a) from a normal distribution N(mu,sigma) (mu,sigma:known) with a condition that the first n values of vector 'a' are known and fixed (basically its fulfilling boundary conditions).
Is there any way I can use Multivariate normal random numbers function: R = mvnrnd(mu,Sigma) or any other method?

Paul on 19 Aug 2021
Yes. If you know mu and Sigma of the vector x and the first n values of x are given, then the density of x(n+1:end) is also normal and can be derived from mu, Sigma, and x(1:n). See this link for the math to get the mean and covariance of x(n+1:end) condtioned on x(1:n), then you can use mvnrnd to generate random numbers of x(n+1:end)
Paul on 23 Aug 2021
I didn't provide an example, so I'm still not sure what you've compared to your code.
Instead of reindexing your problem to fit the formula, it's probably easier to modfiy the formula to fit your problem. Just reverse the 1's and 2's.
mubar = mu2 + Sigma21/Sigma11*(a - mu1);
Sigmabar = Sigma22 - Sigma21/Sigma11*Sigma12;
Feel free to come back if you have any more questions, particularly if you want to post your code with an example. However, if you do, don't use a 10-element vector in the example. Maybe use a 3-element vector X and show the mubar and Sigmabar of X(3) given known values of X(1) and X(2).

R2020b

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