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RE: st: kdensity


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: kdensity
Date   Mon, 25 Apr 2005 21:07:27 +0100

Let's compare like with like. 

-cumul- (official Stata) produces a cumulative distribution, 
leaves it in memory as a variable, 
but does not plot it. 

-distplot- [sic] (SJ) produces a cumulative
distribution on the fly, and does plot it. 
(It can do more than that, which makes it 
more useful, but that is a side issue.)

The underlying calculations are the same. 

If we take your example, suppress the -nograph- 
and insert the -sort- which is needed, then 
it is clearer what is going on: 

sysuse auto

(1) 
kdensity mpg, g(a b) 
cumul b, g(cb)
line cb b, sort 

(2) 
distplot line mpg

What you are doing is comparing 

(1) the integral of a smoothed density function 

(2) a unsmoothed cumulative distribution function. 

(1) is indeed smoother than (2). It would be 
surprising if it were not. But this is nothing 
to do with -cumul- and everything to do with 
what you did with -kdensity-. 

That said, I prefer to get smoother cumulative
distribution functions directly from 
estimated quantiles. 

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

adiallo5@worldbank.org
 
> The cumul command provides a smoother plot than displot.
> 
> e.g.:
> 
> sysuse auto
> kdensity mpg, g(a b) nograph
> cumul b, g(cb)
> line cb b
> displot line mpg
 
Nick Cox
 
> If you want a plot of a (?smoothed) distribution function,
> this is at best a rather indirect route.
> 
> Note first that -distplot- is a program dedicated
> to plotting distribution functions. -search distplot-
> points to locations. It is smart enough that you can
> go directly to something like
> 
> . distplot line Y X
> 
> without doing overlays.
> 
> If the results are not smooth enough, an alternative is
> to base a plot on estimated rather than observed quantiles.
> 
> One command for quantile estimation is -hdquantile-
> from SSC.
> 
> Nick
> n.j.cox@durham.ac.uk
> 
> Amadou Diallo
> 
> > I used to:
> > kdensity X, gen(aa bb) nogr
> > cumul bb, g(cum_bb)
> > ksm cum_bb bb
> > ?
> > If you want the density at each point
> > you could :
> > qui cou
> > local n = r(N)
> > kdensity X, gen(aa bb) nogr n(`n')
> > etc...
> 
> Branko Milanovic
> 
> > When you do kdensity X, STATA charts a kernel density fct 
> of X's. Now,
> > is there a command that would allow me to take the density
> > function thus
> > generated and chart a cumulative density (or distribution) function?
> > Ideally, I would like to do that for both densities, that is
> > to go from a overlay graph
> >
> > twoway (kdensity X) (kdensity Y)
> >
> > To a similar overlay graph of two cumulative density functions.
> >
> > Or is the only way to use:
> >
> > kdensity X, gen(aa bb)
> >
> > And then generate a cumulative function of aa? By the way, I
> > tried that but the graph did not turn out well.
 

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