# st: RE: RE: AW: Calculating area under a curve

 From philippe van kerm To "statalist@hsphsun2.harvard.edu" Subject st: RE: RE: AW: Calculating area under a curve Date Fri, 27 Nov 2009 18:41:34 +0100

```re Qn (1): you can probably use -cumul- and -integ-.  Alternatively you may look at the Generalized Lorenz curve (-ssc install glcurve-) if what you want to do is checking second order stochastic dominance. The Gen Lorenz curve is a plot of the cumulative quantile function and can be used to assess second order stochastic dominance in ways similar to what you would do with integrated CDFs.

re Qn(2): plenty of good references are available -- a good, recent summary can be found here:  http://132.206.230.229/articles/stochdomdp.pdf

Philippe

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: Friday, November 27, 2009 6:15 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: AW: Calculating area under a curve
>
> Just to point out that -cumul- gives you the (cumulated) area under the
> density function. That's what a distribution function is. I don't see
> why you would want to integrate again.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Martin Weiss
>
> Would the -qqplot- recently advertised by NJC not be a good
> alternative? See
> http://www.stata.com/statalist/archive/2009-11/msg01157.html
>
>
> 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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```