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 > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > -- Brian D. Ripley, [EMAIL PROTECTED] 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 ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
