# RE: st: Calculating area under a curve

 From "Nick Cox" To Subject RE: st: Calculating area under a curve Date Fri, 4 Dec 2009 08:55:00 -0000

```Thanks for the clarification, which is very helpful. On a small point of terminology, -cumul- and -integ- are to Stata commands, not functions.

Nick
n.j.cox@durham.ac.uk

I realized after reading your initial post that what I was not on a
producutive path and so I shelved it. I did find the -cumul- and
-integ-  functions ,that I was not aware of, useful for other projects
of mine.

On Thu, Dec 3, 2009 at 12:49 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> It's kind of you to thank us all but you do not distinguish between quite different comments.
>
> Others can speak for themselves for Steve (Samuels) and I couldn't see why this would be interesting or useful. (Steve's at liberty to dissent if that's not his view.) In effect, you are integrating twice, as -cumul- is clearly numerical integration of the density function, even though not named as such, and you then integrate once more.
>
> Could you please explain why this is a good idea?
>
> Nick
> n.j.cox@durham.ac.uk
>
>
> Thank you all (Martin, Philippe, Nick, Steve, Maarten, Bob) for your
> valuable suggestions!
>
> As suggested, I used -cumul- to calculate the cumulative distributions
> and -integ- to calculate the area under the curve..
>
> <pmathru2@illinois.edu> wrote:
>> Dear All,
>>
>> I am analyzing the performance of companies indicated by a variable
>> v1. Variable v1 has a range 0-10 where higher values indicate poorer
>> performance.  I am attempting to compare the performance of companies
>> for the country as a whole and to that at the local level
>> (Metropolitan Statistical Area). I am interested not only in the mean
>> value of v1 but also the variability of v1. One suggestion I got was
>> to compute the cumulative probabilities at the national and local
>> levels and then compare the area under the cumulative probability
>> distributions at the local level to that at the national level.
>>
>> I understand that I can use the -cumul- function in Stata to calculate
>> the cumulative probabilities but I couldn't find a method to calculate
>> the area under the cumulative probability curve. I have two questions
>> in this regard
>> (1) Is there a way in Stata to calculate the area under cumulative
>> probability curve?
>> (2) Could someone point me to reference that I can use to read up on
>> this method?

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