[Octave-bug-tracker] [bug #39768] Improve tcdf() accuracy around x = 0

[Julien Bect]

URL:
  <http://savannah.gnu.org/bugs/?39768>

                 Summary: Improve tcdf() accuracy around x = 0
                 Project: GNU Octave
            Submitted by: jbect
            Submitted on: lun. 12 août 2013 13:29:34 GMT
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: Julien Bect
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.6.4
        Operating System: GNU/Linux

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Details:

The attached bugfix improves the accuracy of tcdf(x, nu) around x = 0.

As an example, for x=1e-5 and nu=2.5, the reference value obtained using
mpmath is 0.50000361808724021 (computations with 100 significant digits, only
17 significant digits shown).

With Octave 3.6.4 I get:

octave:1> format long
octave:2> y = tcdf(1e-5, 2.5)
y =  0.500003618087390
octave:3> yref = 0.50000361808724021
yref =  0.500003618087240
octave:4> err = (y - yref)/yref
err =  2.99313961550892e-13


With the patch applied:

octave:1> format long
octave:2> y = tcdf(1e-5, 2.5)
y =  0.500003618087240
octave:3> yref = 0.50000361808724021
yref =  0.500003618087240
octave:4> err = (y - yref)/yref
err = 0





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File Attachments:


-------------------------------------------------------
Date: lun. 12 août 2013 13:29:34 GMT  Name: jbPatch_tcdf_accuracy.patch 
Size: 3 ko   By: jbect

<http://savannah.gnu.org/bugs/download.php?file_id=28817>

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