From: krishna.myneni@ccreweb.org
On 9/19/24 06:45, Krishna Myneni wrote:
> On 9/19/24 03:57, albert@spenarnc.xs4all.nl wrote:
>> In article ,
>> Krishna Myneni wrote:
>>
>>> Moments of speed
>>> N (m/s) (m/s)^2 (m/s)^3
>>> 10^2 1181.0956 1656472.7 2604709063.
>>> 10^3 1293.3130 1952149.7 3300955817.
>>> 10^4 1259.3279 1862988.3 3108515117.
>>> 10^5 1260.5577 1872157.8 3147664636.
>>> 10^6 1259.4425 1868918.9 3139487337.
>>> 10^7 1259.6136 1869145.0 3139092438.
>>
>> I think for a Monte Carlo simulation at least three tests
>> must be done with different seeds.
>
> Good point. For a meaningful comparison of errors between PRNGs at a
> specific N, the statistical variation of the need to be measured
> for different seed values.
>
> I can add some code to measure this sigma at each N, with 32 seeds
> uniformly spaced between 0 and UMAX.
>
I've calculated the statistical variation in the moments for each set of
N, using 16 different seeds (spaced apart over the interval for UMAX).
The standard dev. for the 16 , computed for N trials is comparable
to the relative error between the moment and its theoretical value.
Thus, the relative errors are indeed a meaningful comparison between the
two prngs tested here, and I think this implies that for N > 10^5 the
LCG PRNG (RANDOM) gives more accurate answers than the KISS 64 bit PRNG
(RAN-KISS), for this problem. The LCG PRNG is faster than the KISS
64-bit PRNG.
minforth stated earlier that he would prefer to use diehard tests to
decide between which of these two PRNGs to use for computing these
results from random trials. It will be interesting to see if diehard
tests are consistent with what I find from actually using the PRNGs and
comparing the results to the expected results (for large N and ideal PRNG).
--
Krishna
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