# Re: st: Calculating area under a curve

 From sjsamuels@gmail.com To statalist@hsphsun2.harvard.edu Subject Re: st: Calculating area under a curve Date Thu, 3 Dec 2009 19:42:00 -0500

```I don't dissent.  I'll just point out that difference in the areas
under two cumulative distribution curves is equal to the difference in
means of the two groups.

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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>

--
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
845-246-0774

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```