# [Rd] pt inaccurate when x is close to 0 (PR#9945)

Duncan Murdoch murdoch at stats.uwo.ca
Wed Oct 10 19:10:32 CEST 2007

```On 10/10/2007 10:35 AM, skylab.gupta at gmail.com wrote:
> Full_Name: Skylab Gupta
> Version: R version 2.5.1 (2007-06-27)
> OS: Windows XP
> Submission from: (NULL) (216.82.144.137)
>
>
> Hello,
>
> I have been playing around with the statistical distributions in R. I think the
> computations for the cumulative distribution function of the students t
> distribution in R are not very accurate.
>
> For instance, the cdf of a students t distribution with 13 degrees of freedom at
> 1e-4 is reported in R as "0.5000391350986764"; from Mathematica, it seems the
> correct value is "0.50003913510150055", only about 9 accurate digits reported in
> R.

As Charles Berry told you when this was posted to R-help, it looks as
though it is Mathematica that is inaccurate.  For example, I would
expect this plot to be smooth, and it is not in either R or Mathematica,
but R is at least monotone:

# the Mathematica values
plot(diff(z[80:100]), type='l')

The R values
plot(diff(pt(1e-4, df=80:100)), type='l')

>
> I also did the following from within R:
>
> -------------
> df<-seq(1,100,by=1)
> y<-pt(1e-4,df)
> 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.
500
>  03969526955183,0.50003969915340063,0.50003970290428668,0.50003970650705731,0.50003970997149927,0.50003971332909936,0.50003971654204993,0.50003971964040972,0.50003972264367180,0.50003972553808163,0.50003972835715427,0.50003973106835642,0.50003973370765664,0.50003973624942966,0.50003973868896101,0.50003974107556448,0.50003974338818691,0.50003974563557085,0.50003974781567961,0.50003974993203681,0.50003975199594708,0.50003975399737965,0.50003975593675354,0.50003975782715593,0.50003975966389691,0.50003976145762119,0.50003976321975063,0.50003976489560775,0.50003976655049909,0.50003976818673812,0.50003976975798736,0.50003977127434285,0.50003977277055756,0.50003977423495483,0.50003977566285773,0.50003977705769798,0.50003977841313474,0.50003977975147973,0.50003978102874791,0.50003978230822732,0.50003978356836509,0.50003978477872879,0.50003978596096421,0.50003978713049724,0.50003978827577344,0.50003978935715154,0.50003979045422919,0.50003979153680134,0.50003979256756137,0.500039793
589
>  57851,0.50003979462027492)
>
> plot(df,(y-z)/z, type="s")
> -------------
>
> In the above R code, df contains the 100 integers between 1-100, y contains the
> cdf of the students t distribution computed at 1e-4 from R, for all the df
> degrees of freedom; and z contains the correct values (to 17 decimal digits) of
> the students t distribution cdf at 1e-4 computed from Mathematica; when I plot
> the relative errors between the computed values from Mathematica and R, it seems
> the relative errors are large; we get only about 10-12 digits of accuracy from R
> rather than about 15 digits (all this assuming that the Mathematica computed
> values are correct).

It seems you are making a bad assumption.

Duncan Murdoch

This happens for all values close to 0 where the cdf is
> evaluated.
>
> I am working on Windows XP, and I installed a precompiled binary version of R.
> The following information might also be useful:
>
> ---------------
>> 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"
>
>> 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)
> ---------------
>
> Is there a reason for this loss of accuracy, or am I missing something here?
> Thanks.
>
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

```