From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Fri 16 Dec 2005 - 05:29:44 EST

Date: Fri 16 Dec 2005 - 05:29:44 EST

On Thu, 15 Dec 2005, Thomas Lumley wrote:

> On Thu, 15 Dec 2005, Phineas wrote:

*>
**>> How many distinct values can rnorm return?
**>
**> 2^32-1. This is described in help(Random)
*

Mot for the default method for rnorm, as it uses two runif's. The answer is somewhere in the 2^50s, as the base uniform random number uses 2^59 but some will be mapped to the same result.

>> I assume that rnorm manipulates runif in some way, runif uses the Mersenne

*>> Twister, which has a period of 2^19937 - 1. Given that runif returns a 64
**>> bit precision floating point number in [0,1], the actual period of the
**>> Mersenne Twister in a finite precision world must be significantly less.
**>
**> No. Not at all. Consider a sequence of 1-bit numbers: individual values
**> will repeat fairly frequently but the sequence need not be periodic with
**> any period
**> 1101001000100001000001
**> is the start of one fairly obvious non-periodic sequence.
**>
**> There are reasons that a longer period than 2^32 is useful. The most
**> obvious is that you can construct higher-resolution numbers from several
**> runif()s.
*

And the default method for rnorm does so.

> The Mersenne Twister was designed so that quite long

*> subsequences (623 elements) would be uniformly distributed.
**>
**> Less obvious is that fact that a periodic pseudorandom sequence is likely
**> to show a frequency distribution of repeat values that differs from the
**> random sequence once you get beyond about the square root of the period.
**> This means that a 32-bit PRNG should really have a period of at least
**> 2^64.
**>
**> The randaes package provides a runif() that uses 64 bits to construct a
**> double, providing about 53 bits of randomness.
**>
**>> One of the arguments for Monte Carlo over the bootstrap is that for a sample
**>> size n the bootstrap can return at most 2^n distinct resamples, however for
**>> even for relatively small sample sizes there may be no increase in precision
**>> in using Monte Carlo.
**>
**> I don't get this at all. What technique are you comparing to the bootstrap
**> and for what purpose?
**>
**> -thomas
**>
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*

-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Fri Dec 16 05:46:40 2005

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