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New algorithm for random number generation - Namir - 05-26-2014 01:04 AM
I have been tinkering with a set of new algorithms for uniformly-distributed random number generation (RNG). I test each algorithm using several long runs. I test various statistics related to each run of 10000 numbers (such as auto-correlation and various histograms). I end up calculator an empirical "goodness" factor based on these statistics.
Recently I bumped into an interesting algorithm while working with a family of RNGs that use ratios of random numbers generated using simpler/basic methods. I noticed the following:
Code:
1. Generate r1 (between 0 and 1) using basic RNG algorithm #1
2. Generate r2 (between 0 and 1) using basic RNG algorithm #2
3. Calculate R -= r1/r2
4. If R > 1 then R = 1/R
5. If R = 1 then R = 0
6. Return R as a random numberI noticed that the above algorithm often generates better random number than the underlying basic RNG algorithms.
I will publish (on my web site) my tinkering in a few week.
Namir
PS: You have some flexibility in choosing the basic algorithms in steps 1 and 2.
RE: New algorithm for random number generation - Garth Wilson - 05-26-2014 04:00 AM
If the random numbers are needed at random times, you can involve a reading of the timer as part of the algorithm. The word TIME on the HP-71 gives seconds since midnight, with .01s resolution.
RE: New algorithm for random number generation - Paul Dale - 05-26-2014 04:04 AM
Times are usually a bad idea in random number generators.
Time isn't very random and it destroys any repeatability.
Seeding using time as a component needn't be such a bad thing.
- Pauli
RE: New algorithm for random number generation - Namir - 05-26-2014 06:53 PM
I have designed[/b] RNGs using virtual clocks and virtual timers. Each time you call the RNG of these types, the clock/timer ticks forward by one virtual second. This makes the code independent of the underlying system's clock speed. Using virtual clocks and timers you can define the range of seconds, minutes, hours, days, and months to YOUR LIKING and not be forced to use conventional ranges.
Namir
RE: New algorithm for random number generation - ttw - 06-06-2014 01:31 AM
Note that if the input RNGs are uniform over (0-1) then the output isn't. This method is useful in generating Gaussians and the like by sampling from a restricted domain followed by rejection. It goes by the name "ratio uniforms method."