Hi everyone,
I am working on analyzing renewable energy effect in electrical systems. I use Monte Carlo simulation to find the desired electrical variables. I want to consider the effect of co-relation between the input variables i.e between different generators or loads or between generators and loads. I already have constructed a co-relation matrix which I have taken from the literature. So, How can I consider these co-relation or How can I modify my existing algorithm to consider this effect?
Thank you in advance,
Sam
@ Samundra Gurung
Dear sir,
Frankly, it is hard to understand what you are asking for. Let me guess, that the problem is how to generate family of a fixed number of random variables given their pd (probability distribution) AND their covariance matrix. If this is so, then the simplest possibility is to use normal variables generated with the use of eigenvectors of the covariance matrix or Cholesky decomposition of covariance matrix, comp..
https://stats.stackexchange.com/questions/38856/how-to-generate-correlated-random-numbers-given-means-variances-and-degree-of
You can search for other material by MsWiki under tags: generating correlated random variables.
If you need positive exponential correlated rv-s, then some particular constructions are possible based on minmax operations. This is a particularly efficient method if the resulting variables are"times to failure" correlated due to existence of common factor influencing their "life-time".
EXAMPLE. Two eponential rv-s X and Y with mean value m with correlation r \in (0,1), can be obtained by the algorithm
X =min{Z1,Z_2}, Y = min {Z2,Z3}
where Z1, Z2, Z3 are exponential with mean values m1, m2 and m3=m1 such that
m = m1*m2/(m1 + m2) and r = F(m1,m2)
where F is some easily calculable function, cf. the book by Richard E. Barlow, Frank Proschan: Statistical theory of reliability and life testing: probability models, Holt, Rinehart and Winston, 1975, 290.
Disadvantage of such modelsl is that X=Y holds with positive probability.
Hopefully, this helps,
Regards, Joachim
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