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RE: st: RE: Percentiles: Identify of smallest observation closet to percentile value


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Percentiles: Identify of smallest observation closet to percentile value
Date   Tue, 4 Feb 2003 10:08:13 -0000

Ronnie Babigumira
> 
> Rod, this works for me
> . sum p, d
> 
>                             Price
> -------------------------------------------------------------
>       Percentiles      Smallest
>  1%         3291           3291
>  5%         3748           3299
> 10%         3895           3667       Obs                  74
> 25%         4195           3748       Sum of Wgt.          74
> 
> 50%       5006.5                      Mean           6165.257
>                         Largest       Std. Dev.      2949.496
> 75%         6342          13466
> 90%        11385          13594       Variance        8699526
> 95%        13466          14500       Skewness       1.653434
> 99%        15906          15906       Kurtosis       4.819188
> 
> . list make price if price == `r(p75)'
> 
>      make                   price
>  23. Dodge St. Regis        6,342
> 
> **
> You may or may not use ur own macro. If u use ur own macro, the 
> after sum p, d, you could 
> 
> local p75 = r(p75) (I notice u missed this step)
> and then list
> 
> list make price if price == `p75'
> 

As noted previously, this works because, for this sample 
size, the quantile in question is a particular value
and thus at least one value is equal to it. But 
as the documentation for -summarize- explains, some 
quantiles are computed by splitting the difference 
between adjacent order statistics. 

Try 

. sysuse auto 
. drop in 1/2
. su displ, d

The upper quartile is calculated as (231 + 250) / 2
and is not equal to any observed value. This 
necessitates an approach based on finding whatever 
minimises |value - quantile| = abs(value - quantile)
and several observations may tie on this criterion 
(even if there are no ties in the data). 

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

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