Re: rand("state")

[Mike Miller]

On Wed, 15 Feb 2006, Mike Miller wrote:

> On Wed, 15 Feb 2006, Paul Kienzle wrote:
>
> > You don't get any improvement in the randomness by using longer seeds.
>
> That is interesting.  The one thing I don't understand is why there is a 
> 625-integer state if I get no improvement in randomness for using 625 
> integers for the seed instead of a single integer.  I'm probably 
> confusing "state" and "seed."  With a period of about 4.3*10^6001, I 
> would think that using a seed that is always less than 10^9 would be 
> allowing the user to access only a small minority of the random 
> sequences available.


I just did something else to test how this works.  It seems to me that use 
of a single 32-bit integer seed works and is fine for many applications. 
Use of a single integer doesn't change the quality of the random numbers 
produced and it is easier to deal with.  However, the single integer seed 
limits the number of possible pseudorandom starting sequences to 2^32. 
Use of the full 624 32-bit integers (plus the position integer) allows for 
all possible 2^19936 starting sequences.

If you will be producing many random replicates in a simulation study, it 
is better to use the full 625-integer seed so that the probability of any 
two replicates being identical is extremely small.

Do I have this right?

Mike



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