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MathGroup Archive 1992

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Integrating Normal Distributions gives the wrong answer

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Integrating Normal Distributions gives the wrong answer
  • From: mek at guinan.psu.edu (Mark E. Kotanchek)
  • Date: Tue, 8 Sep 92 16:58:04 EDT

I was intending to as y'all about the suitability of running Mma 2.1 on a  
Mac Powerbook 170 since I was working at home over the weekend trying to  
figure out convergence rates of covariance matrices; alas, now that I'm  
playing with Mma 2.0 on my office NeXTstation, I'm wondering whether I  
should spring for Maple and avoid the "beautifully formatted, incorrect  
answers" syndrome which my colleague is chortling about at the moment.

The issue is integrating normal distribution functions. Given that I define  
the Gaussian density function,

   f=Exp[-(x-mu)^2/(2 sigma^2)]/(sigma Sqrt[2 Pi])  

   

which gives me
   

                      1
   ---------------------------------------
             2         2
    (-mu + x) /(2 sigma )
   E                      Sqrt[2 Pi] sigma
   

upon integrating from negative to positive infinity I should get a result of  
1. Instead Mathematica assures me that the answer is zero!!

   Integrate[f,{x,-Infinity,Infinity}]

   0

Setting mu = 0 leads to the result,

   mu=0;
   Integrate[f,{x,-Infinity,Infinity}]

     sigma
   ----------
   Abs[sigma]

which, is closer and presumably Mathematica would give me the correct result  
if I knew how to tell Mathematica that sigma is always non-negative. (A  
feature which I'm sure must be in Mathematica but manages to elude me while  
scouring Blachman's various books and Wolfram's manual--obtuse documentation  
of an obtuse program overcomes me once more!)

Anyhow, is this misbehavior of Mathematica fixed in v2.1 or is there some  
sort of a rationale for such behavior? It seems like I'm trying such a  
simple exercise that there isn't much room for operator error....

Thanks much,

Mark.
---
Mark Kotanchek
Guidance & Control Dept - 363 ASB
Applied Research Lab/Penn State
P.O. Box 30
State College, PA 16804

e-mail:	mek at guinan.psu.edu (NeXTmail)
TEL:	(814)863-0682
FAX:	(814)863-7843





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