There are several arbitrary precision packages available: gmp (an interface to the GNU multi-precision library on CRAN) and bc (an R interface to the bc arbitrary precision calculator): http://r-bc.googlecode.com
There are also packages providing R interfaces to two computer algebra systems and they both support not only arbitrary precision but also exact calculation: http://rsympy.googlecode.com http://ryacas.googlecode.com > library(bc) > 1 - (1-10^-75)^10 [1] 0 > bc("1 - (1-10^-75)^10") [1] ".0000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000" On Thu, May 21, 2009 at 10:15 AM, Mark Bilton <mcbil...@hotmail.com> wrote: > > I am having a slight problem with probabilities. > > To calculate the final probability of an event p(F), we can take the product > of the chance that each independent event that makes p(F) will NOT occur. > So... > p(F) = 1- ( (1-p(A)) * (1-p(B)) * (1-p(C))...(1-p(x)) ) > > If the chance of an event within the product occurring remains the same, we > can therefore raise this probability to a power of the number of times that > event occurs. > e.g. rolling a dice p(A) = 1/6 of getting a 1... > p(F) = 1 - (1- (1/6))^z > p(F) = 1 - (1-p(A))^z tells us the probabiltity of rolling a 1 'at least > once' in z number of rolls. > > So then to R... > > if p(A) = 0.01; z = 4; p(F) = 0.039 > > obviously p(F) > p(A) > > however the problem arises when we use very small numbers e.g. p(B) = 1 * > 10^-30 > R understands this value > However when you have 1-p(B) you get something very close to 1 as you > expect...but R seems to think it is 1. > So when I calculate p(F) = 1 - (1-p(B))^z = 1 to the power anything equals 1 > so p(F) = 0 and not just close to zero BUT zero. > It doesn't matter therefore if z = 1*10^1000, the answer is still zero !! > > Obviously therefore now p(F) < p(B) > > Is there any solution to my problem, e.g. > - is it a problem with the sum (-) ? ie could I change the number of bits the > number understands (however it seems strange that it can hold it as a value > close to 0 but not close to 1) > -or should I maybe use a function to calculate the exact answer ? > -or something else > > Any help greatly appreciated > Mark > - > > > > > > _________________________________________________________________ > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
