Given the following decomposition
where , is constant, and are independent standard normal random variables,
the goal is to estimate the target function
where is scalar in (-4,-1).
I calculated the target function by simulating Z and Y for M=10,000, N = 10 and 100,000 simulations in R and Matlab. The results are very different: Matlab produces almost twice higher results, which makes me wonder if Matlab's random number generator is able to produce more extreme values comparing to R.
BTW, I use rnorm() in R and normrand() in Matlab to generate random numbers.
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