Integration of cumulative distribution function.

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Jeffrey Turner - 27 Dec 2006 10:32 GMT

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

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Jeffrey Turner - 28 Dec 2006 09:51 GMT

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@gmail.com]
Sent: Wednesday, December 27, 2006 7:38 AM
To: Jeffrey Turner
Subject: Re: Integration of cumulative distribution function.

> 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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Jean-Marc Gulliet - 28 Dec 2006 09:59 GMT

> 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
[quoted text clipped - 6 lines]
> Thanks,
> Jeff

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Math Forum / Math Software / Mathematica / December 2006

Integration of cumulative distribution function.