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MathGroup Archive 2006

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RE: Integration of cumulative distribution function.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72443] RE: Integration of cumulative distribution function.
  • From: "Jeffrey Turner" <turner at finnecon.com>
  • Date: Thu, 28 Dec 2006 04:59:51 -0500 (EST)

 
Thanks for the help.  I got a result but I am now curious about the Erf
piece of my result.  I looked at the help file and it states that the
Erf[z] is the integral of the Gaussian distribution, but shouldn't the
integral have (-t^2)/2 instead of -t^2?

Thanks,

Jeff


-----Original Message-----
From: Jean-Marc Gulliet [mailto:jeanmarc.gulliet at gmail.com] 
Sent: Wednesday, December 27, 2006 7:38 AM
To: Jeffrey Turner
Subject: [mg72443] Re: Integration of cumulative distribution function.

Jeffrey Turner wrote:
> I am new to mathematica and I am looking to integrate the cumulative 
> distribution function.  I am looking to integrate from 0 to T where
> sigma and mu vary by time.   I am not sure how to set this up.  If I
use
> mu * t and for mu and sigma * square root of t for sigma mathematica 
> just returns what I type in.  So for 
> integrate[CDF[mu*t,sigma*t^.5],{0,T}] just returns what I typed in.  I

> am looking for any help.
> 
> Thanks,
> Jeff
> 

Hi Jeff,

In order to use functions such as CDF, you must first load the package
that contains their definitions. You can use Needs or Get.

Needs["Statistics`NormalDistribution`"]

Second, Mathematica built-in functions start with capital letter. 
Moreover you have forgotten to type in the name of the integration
variable. Also, it is usually better to use exact values when possible.

Integrate[CDF[mu*t, sigma*t^(1/2)], {t, 0, T}]

Happy holidays,
Jean-Marc


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