On Wed, 3 Oct 2007, skylab gupta wrote: > Hello, > > I have been playing around with the statistical distributions in R, and > overall I think the accuracy is very good. However, it seems that for the > Student's t distribution, the CDF loses accuracy when evaluated at values > close to zero. For instance, I did the following in R > > ---------------------------------- > df<-seq(1,100,by=1) > z<-c(0.50003183098839799,0.50003535533895194,0.50003675525997071, > 0.50003749999985481,0.50003796066840744,0.50003827327749706, > 0.50003849914427922,0.50003866990364754,0.50003880349244212 , > 0.50003891083995444,0.50003899897813187,0.50003907263208447, > 0.50003913510150055,0.50003918874627440,0.50003923531785055, > 0.50003927612461441,0.50003931217478748,0.50003934425324170, > 0.50003937297989520,0.50003939886014204, 0.50003942229165621, > 0.50003944360703978,0.50003946308016112,0.50003948094039441, > 0.50003949738053710,0.50003951256485324,0.50003952663295181, > 0.50003953969680248,0.50003955185925653,0.50003956322006460, > 0.50003957385523301,0.50003958382054481 ,0.50003959318443636, > 0.50003960200394315,0.50003961032679112,0.50003961818144815, > 0.50003962562026172,0.50003963266089213,0.50003963934773465, > 0.50003964569404735,0.50003965173577758,0.50003965749688895, > 0.50003966298323521, 0.50003966823056478,0.50003967322766096, > 0.50003967801868676,0.50003968260005904,0.50003968700228751, > 0.50003969121916547,0.50003969526955183,0.500039699153400 > 63,0.50003970290428668,0.50003970650705731,0.50003970997149927 , > 0.50003971332909936,0.50003971654204993,0.50003971964040972, > 0.50003972264367180,0.50003972553808163,0.50003972835715427, > 0.50003973106835642,0.50003973370765664,0.50003973624942966, > 0.50003973868896101,0.50003974107556448, 0.50003974338818691, > 0.50003974563557085,0.50003974781567961,0.50003974993203681, > 0.50003975199594708,0.50003975399737965,0.50003975593675354, > 0.50003975782715593,0.50003975966389691,0.50003976145762119, > 0.50003976321975063,0.50003976489560775 ,0.50003976655049909, > 0.50003976818673812,0.50003976975798736,0.50003977127434285, > 0.50003977277055756,0.50003977423495483,0.50003977566285773, > 0.50003977705769798,0.50003977841313474,0.50003977975147973, > 0.50003978102874791, 0.50003978230822732,0.50003978356836509, > 0.50003978477872879,0.50003978596096421,0.50003978713049724, > 0.50003978827577344,0.50003978935715154,0.50003979045422919, > 0.50003979153680134,0.50003979256756137,0.50003979358957851, > 0.50003979462027492 ) > y<-pt(1e-4,df) > plot(df,(z-y)/z, type="s") > ---------------------------------- > > Basically, I evaluate the CDF of the Student's t distribution at 1e-4, for > integer degrees of freedom from 1 to 100; the variable y contains the values > computed by R, and the variable z contains the values obtained by > Mathematica (with about 17 digits precision). The plot of relative accuracy > shows that we get only about 10 digits of accuracy with R. It seems there is > something is going wrong in the computations. Is this correct, or am I > missing something?
How did you verify the accuracy of the vector z ? The differences in z are not monotone. Your worst case is df=88 Looks like pt() is better there , but both have error on the order of 1e-11: > integrate( function(x) dt(x,88), 0, 1e-4 ) 3.978106e-05 with absolute error < 4.4e-19 > z[88] -0.5 - integrate( function(x) dt(x,88), 0, 1e-4 )$value [1] -2.661810e-11 > pt( 1e-04, 88 ) - 0.5 - integrate( function(x) dt(x,88),0,1e-4)$value [1] 1.224781e-11 HTH, Chuck > > I am using a precompiled binary version of R on windows xp. Following > information might be helpful as well > > ---------------------------- >> version > _ > platform i386-pc-mingw32 > arch i386 > os mingw32 > system i386, mingw32 > status > major 2 > minor 5.1 > year 2007 > month 06 > day 27 > svn rev 42083 > language R > version.string R version 2.5.1 (2007-06-27) > >> sessionInfo() > R version 2.5.1 (2007-06-27) > i386-pc-mingw32 > > locale: > LC_COLLATE=English_United States.1252;LC_CTYPE=English_United > States.1252;LC_MONETARY=English_United > States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252 > > attached base packages: > [1] "stats" "graphics" "grDevices" "utils" "datasets" "methods" > "base" >> > ---------------------------- > > Any help is appreciated. > > Thanks. > > [[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. > Charles C. Berry (858) 534-2098 Dept of Family/Preventive Medicine E mailto:[EMAIL PROTECTED] UC San Diego http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901 ______________________________________________ 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.
