Find out what centile of a distribution a given value represents

[Castor Comploj]

I have a distribution (income). I would like to find out what percentile a given income (e.g. 500 USD) represents (and include this in a .do file to share with collaborators). Is this possible with an integrated Stata function?

[Carlo Lazzaro]

Castor:
do you mean something along the following lines?

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. help centile

. centile ln_wage , centile(10(10)90)

                                                          Binom. interp.   
    Variable |       Obs  Percentile    Centile        [95% conf. interval]
-------------+-------------------------------------------------------------
     ln_wage |    28,534         10    1.166102        1.157089    1.168778
             |                   20    1.301507        1.297063    1.308635
             |                   30    1.420336        1.410987    1.428017
             |                   40    1.530165         1.52287    1.536367
             |                   50    1.640541        1.633343    1.647948
             |                   60    1.758746        1.753038    1.764279
             |                   70     1.88922         1.87977    1.896542
             |                   80    2.048963         2.04157    2.058625
             |                   90     2.27569        2.266884    2.284872

. sum ln_wage

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
     ln_wage |     28,534    1.674907    .4780935          0   5.263916

.

[Castor Comploj]

Ciao Carlo, No. The above can be easily found online.
My question is: what exact percentage of the sample has an ln_wage below 1.147 (in the above example).

[FernandoRios]

Hi Castor
There are perhaps 2 options for that.
1) using the Empirical distribution:

gen w1 = lnwage<1.147
gen w2 = lnwage<=1.147
sum w1 w2
that will give you two alternatives of the Percentiles associated with 1,147 in your data. I use < and <= because I have seen both definitions for quantiles.
The other option is Estimating the CDF (F(lnwage)) using semiparametric approach (like what kdensity do but for CDF not PDF). And then simply extrapolate F for 1.147

If you want to use integrals, this is also possible, using kdensity and integ

use http://fmwww.bc.edu/RePEc/bocode/o/oaxaca.dta
kdensity lnwage, gen(fd) at(lnwage)
integ fd lnwage if lnwage<=2

HTH

[Nick Cox]

https://www.stata.com/support/faqs/s...ing-positions/ gives further discussion.