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MathGroup Archive 1998

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be aware!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14140] be aware!
  • From: Zvi Wiener <mswiener at mscc.huji.ac.il>
  • Date: Mon, 28 Sep 1998 03:51:52 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Steve:
Below is my message to the Mathematica newsgroup.
************************************************************* When
calculating the standard normal distribution I have discovered some
very strange behavior of Mathematica 3.0.1 on PC.  Note that the 3 ways
below must be equivalent:


subst={mu->0.2,sg->1.2};
Integrate[Exp[-((z-mu)/sg)^2/2],{z,-Infinity,-0.1}]/Sqrt[2Pi]/sg/.subst
Integrate[Exp[-((z-mu)/sg)^2/2],{z,-Infinity, 0}]/Sqrt[2Pi]/sg/.subst
Integrate[Exp[-((z-mu)/sg)^2/2],{z,-Infinity, 0.1}]/Sqrt[2Pi]/sg/.subst
Out[]=0.401294
Out[]=0.433816
Out[]=0.400839	<----------- note this number!


m=0.2;
s=1.2;
Integrate[Exp[-((z-m)/s)^2/2],{z,-Infinity,-0.1}]/Sqrt[2Pi]/s
Integrate[Exp[-((z-m)/s)^2/2],{z,-Infinity, 0}]/Sqrt[2Pi]/s
Integrate[Exp[-((z-m)/s)^2/2],{z,-Infinity, 0.1}]/Sqrt[2Pi]/s

Out[]=0.401294
Out[]=0.433816
Out[]=0.466793


Needs["Statistics`ContinuousDistributions`"];
CDF[NormalDistribution[mu,sg]/.subst,-0.1]
CDF[NormalDistribution[mu,sg]/.subst, 0]
CDF[NormalDistribution[mu,sg]/.subst, 0.1]

Out[]=0.401294
Out[]=0.433816
Out[]=0.466793

Note that the third number (0.317757) is wrong! It is smaller that the
previous two, although it is an integral of a positive function over a
strictly bigger interval.
I understand that it is very difficult to integrate a function over an
infinite interval, but I am amazed that there was no warning.  I
suggest somebody at Wolfram to fix it.

Zvi Wiener.
****************************************************************** Zvi
Wiener					Business School
e-mail: mswiener at mscc.huji.ac.il		Hebrew University tel:
972-2-588-3049				Mount Scopus
fax: 972-2-588-1341				Jerusalem 91905
http://pluto.huji.ac.il/~mswiener/zvi.html	ISRAEL
******************************************************************


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