MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

More Integrate woes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9584] More Integrate woes
  • From: NOHAMcrose at c2.telstra-mm.net.au (Colin Rose)
  • Date: Thu, 13 Nov 1997 01:40:48 -0500
  • Organization: Theoretical Research Institute
  • Sender: owner-wri-mathgroup at wolfram.com

In any statistical setting, calculation of the  Gaussian distribution
function is extremely important. Under Mathematica v3, this is
something of a disaster.

 
To summarise the problem:

Under v3:
________

Expressions such as:

     aa = Integrate[Exp[-x^2],{x,-Infinity,y},
GenerateConditions->False]

return output *of form*:

     1 - Erf[Sqrt[y^2]]
    
Our user now seeks numerical output. S/he enters:

     (aa /.  y -> 3) == (aa/. y -> -3)
     True

This is clearly FALSE. 


BY CONTRAST, under v2.2: 
_______________________

    aa = Integrate[Exp[-x^2],{x,-Infinity,y}]

returned output of form:

    1 + Erf[y]

which is correct for all real y. No problem.


________

The problem with v3 here is not only that setting 
  
   GenerateConditions->False

yields incorrect results for one of the most important and common
integration problems, but that even if we set
 
   GenerateConditions->True

the resulting conditional statement treats the distribution as if it is
asymmetrical, when the normal distribution itself is  clearly
symmetrical. For instance:

  aa = Integrate[Exp[-x^2],{x,-Infinity,y}, GenerateConditions->True]

returns

  If[ y < 0,     

      -(1/2)*Sqrt[Pi]*(-1 + Erf[Sqrt[y^2]])  , 
      
      Integrate[E^(-x^2), {x, -Infinity, y}]
    ]

Choosing y < 0 as opposed to y > 0 as a basis for conditional output is
completely arbitrary, and precisely the cause of the
GenerateConditions->False bug.


It would be great to hear that this will be fixed in v3.1.

  [ Co-author Murray Smith discovered these oddities 
    and has been cursing wolfies ever since. ]


Cheerio

Colin

-- 
Colin Rose 
tr(I) - Theoretical Research Institute
______________________________________ NOHAMcrose at c2.telstra-mm.net.au
http://www.usyd.edu.au/su/tri/



  • Prev by Date: memory management
  • Next by Date: Evaluating Many Notebooks
  • Previous by thread: memory management
  • Next by thread: Re: More Integrate woes