Hi! I am doing some computer experiments with Gumbel random numbers. 1) According to the books and manuals:
CALL STREAMINIT(2); X= RAND("GUMBEL", MY, SCALE); An alternative: Xi= MY - SCALE*LOG( -LOG(RAND('UNIFORM')));
These two seem to produce results that are identical. I have used both to produce a lot of random numbers. Works fine. Then I calculated the Mean, StdDev and a lot of quantiles.
2) An alternative, when producing many random numbers is the following: X= MY - SCALE*LOG(-LOG(Step)); where Step is the index in a do-loop. 5Mi values. Then I calculated the Mean, StdDev and a lot of quantiles. The values are almost the same as above, with very small differences, Fine - OR?
When I look at the values generated using 2) in some small intervals e.g. around the median the values look very smooth and nice. When I do the same using the values produced by 1) the values are not at all that smooth, but vary up and down. Question: Is this described in any paper? Are the values produced in 2) also random numbers.
I would appreciate some comments and advice on this matter.
Best Regards AndersS
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