Multiple (two) CDF's one graph

[Sotia Xanalatou]

Hi,

I am trying to plot two (or more) cdf's in a single graph. I prefer the form of a stairstep connected line and I am trying the following options but I get only one out of the cdf's properly connected.
The levels also in the y-axis are not correct.

1- I am getting the line connection properly for both line graphs but not when I try to combine them in a single graph

cumul x if y==1, gen(cumy1)
sort cumy1
line cumy1 x, sort c(J) m(J)
cumul x if y==0, gen(cumy0)
sort cumy0
line cumy0 x, c(J) m(J)
twoway (line cumy1 x, sort c(J) m(J)) (line cumy0 y, c(J) m(J))

2- Similar unsuccessful attempt when I try to use "line || line" etc.

cumul x if y==1, gen(cumy1)
sort cumy1
line cumy1 x, sort c(J) m(J)
cumul x if y==0, gen(cumy0)
sort cumy0
line cumy0 x, c(J) m(J)
line cumy1 x, sort c(J) m(J) || line cumy0 y, c(J) m(J)

3- Using the "stack" command

cumul x if y==1, gen(cumy1)
cumul x if y==0, gen(cumy0)
stack cumy1 x if y==1 cumy0 x if y==0, into(x y) wide clear
line cumy1 cumy0 x, c(J J) m(J J) sort ylab(, grid) ytitle("") xlab(, grid)

I have tried as well to first sort x and y and later on generate the cumulative function with a similar result.

I also would like to add features as lcolor(black) lpattern(dash) graphregion(color(white)) bgcolor(white) aspect(1), titles of y-axis and x-axis but I am posting above only simple versions of my code as I need to get first the cdf's properly plotted. However, if I am not mistaken, I double the options if "stack" is used i.e. lcolor(black black) lpattern(dash solid) while using separately in the case of a "twoway line" or "line || line" graph type, right ?

Any particular help on how I can such an unified graph would be appreciated.

Thank you,

Sotia

[Nick Cox]

I could explain in detail what is wrong here but I imagine that you will be happier knowing that community-contributed commands have existed to do this for at least 20 years. I will write about the one I know best. distplot is downloadable from the Stata Journal website.

Typing

search distplot, historical

will yield in an up-to-date Stata

SJ-19-1 gr41_5  . . . . . . . . . . . . . . . . . Software update for distplot
        (help distplot if installed)  . . . . . . . . . . . . . . .  N. J. Cox
        Q1/19   SJ 19(1):260
        changes include better handling of the by() option calls;
        simpler default y-axis titles; more detailed discussion of
        exactly what is plotted; and more information on ridits

SJ-10-1 gr41_4  . . . . . . . . . . . . . . . . . Software update for distplot
        (help distplot if installed)  . . . . . . . . . . . . . . .  N. J. Cox
        Q1/10   SJ 10(1):164
        new reverse(ge) option specifies plotting probabilities or
        frequencies greater than or equal to any data value

SJ-5-3  gr0018  . . . . . . . . . .  Speaking Stata: The protean quantile plot
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        Q3/05   SJ 5(3):442--460           (see gr41_3 and gr42_3 for commands)
        discusses quantile and distribution plots as used in
        the analysis of species abundance data in ecology

SJ-5-3  gr41_3  . . . . . . . . . . . . . . . . . Software update for distplot
        (help distplot if installed)  . . . . . . . . . . . . . . .  N. J. Cox
        Q3/05   SJ 5(3):471
        simplified syntax; both by() and over() are now allowed

SJ-4-2  gr0004  .  Speaking Stata: Graphing categorical and compositional data
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        Q2/04   SJ 4(2):190--215                                 (no commands)
        discusses graphical possibilities for categorical and
        compositional data

SJ-4-1  gr0003  . . . . . . . . . . . . Speaking Stata: Graphing distributions
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        Q1/04   SJ 4(1):66--88                                   (no commands)
        a review of official and user-written commands for
        graphing univariate distributions; includes tricks
        beyond what is obviously and readily available

SJ-3-4  gr41_2  . . . . . . . . . . . . . . . . . Software update for distplot
        (help distplot if installed)  . . . . . . . . . . . . . . .  N. J. Cox
        Q4/03   SJ 3(4):449
        option tscale() renamed as trscale()

SJ-3-2  gr41_1  . . . . . . . . . . . . . . . . . Software update for distplot
        (help distplot if installed)  . . . . . . . . . . . . . . .  N. J. Cox
        Q2/03   SJ 3(2):211
        enhanced to use Stata 8 graphics and provides new options

STB-51  gr41  . . . . . . . . . . . . . . . . . .  Distribution function plots
        (help distplot if installed)  . . . . . . . . . . . . . . .  N. J. Cox
        9/99    pp.12--16; STB Reprints Vol 9, pp.108--112
        plots the cumulative distribution function or survival function
        and allows multiple variables

The articles from 1999 and 2004 may still be of interest -- the key principles here go back many decades -- and are directly accessible at

https://www.stata.com/products/stb/journals/stb51.pdf

https://www.stata-journal.com/articl...article=gr0003

but software (do and help) should be downloaded from the latest source, as I write Stata Journal 19(1) 2019. Note particularly that the syntax has changed over time.


Here's a token example with some technique.

. sysuse auto, clear
(1978 Automobile Data)

. distplot mpg, over(foreign) scheme(s1color) c(J J) lc(red blue) yla(0 "0" 1 "1" 0.2(0.2)0.8, format ("%02.1f") ang(h))

Although I've kept tinkering with this, I much prefer quantile plots for most applications, for which qplot (Stata Journal) is one vehicle and stripplot (SSC) is another.

[Mukesh Punia]

Dear Nick Cox is it possible to add the Theoretical CDF in the distplot in the above example? I looked for the same using Ben Jann 's dstat as well. This further does not allow by option with over for CDF. I am using STATA 18.


Thank you - Mukesh

[Nick Cox]

Absolutely. What is likely to be most useful is the scope to use addplot() to call up twoway function.

sysuse auto, clear 
distplot mpg, c(J)  addplot(function normal((x - 21.3) /  5.786), ra(mpg)) legend(order(1 "data" 2 "normal")) xtitle("`: var label mpg'")

gives a plot of the cumulative normal with the same mean and SD as the data.

That said, a dedicated quantile-quantile plot is immensely more advisable here.

[Mukesh Punia]

Thank you Nick Cox for your response!

My issue is adding normal with by option;

  distplot y,  by( x1)

* Example generated by -dataex-. For more info, type help dataex
clear
input float y byte x float x1
-1.33 1 1
-1.41 1 1
 -1.9 1 1
  .67 2 1
  1.4 2 1
 2.09 2 1
-1.83 2 1
 -.44 1 1
  .19 2 1
 -2.2 2 1
-1.21 1 1
  .39 2 1
 -.94 1 1
 -.78 1 1
 -1.8 2 1
 1.69 1 1
  .24 2 1
 -.86 1 1
  .33 1 1
 -.57 1 1
-1.63 2 1
 2.61 2 1
  1.2 2 1
  .08 2 1
  .11 2 1
 -.22 2 1
-3.69 1 1
-1.43 1 1
  1.4 1 1
  .96 2 1
  .68 1 1
 -.17 2 1
  -.7 1 1
-1.06 2 1
  .84 1 1
-1.93 2 1
  .81 1 1
 1.91 1 1
-1.13 1 1
  .08 2 2
-1.31 1 2
 -.15 2 2
  .21 2 2
-2.45 1 2
-1.08 2 2
 5.88 2 2
  .11 2 2
 1.34 2 2
 -.02 1 2
-2.16 1 2
  .19 1 2
 1.98 2 2
 2.58 1 2
 2.13 1 2
-2.08 2 2
    0 1 2
  4.1 1 2
-2.86 2 2
-2.49 2 2
-2.07 1 2
 -2.4 2 2
-1.86 1 2
-1.95 1 2
  .95 1 2
 -.51 2 2
-2.13 2 2
-1.86 1 2
 -.41 1 2
 -4.2 1 2
-1.99 1 2
  .14 2 1
 -.98 1 1
   -2 2 1
 -.99 2 1
 5.49 1 1
  -.8 1 1
 1.29 1 1
 -.65 2 1
-1.42 1 1
-1.06 2 1
-1.67 2 1
  .96 1 1
-1.33 2 1
 -2.4 1 1
  .04 2 1
 -.97 2 1
 -.49 2 1
 1.05 1 1
-1.64 2 1
  1.6 2 1
  .13 2 1
 -1.2 2 1
-2.51 2 1
  .27 1 1
 -.83 2 1
-1.26 2 1
-1.09 1 1
  .32 2 1
-3.37 2 1
-1.52 2 1
end

[Nick Cox]

So what does that mean in detail: the same mean and SD, different mean and SD? Or?

[Nick Cox]

Nothing stops you adding two curves to a distplot, but as before I'd recommend quantile-normal plots. Here I use qplot from the Stata Journal, a scale on which normal distributions would plot on straight lines and added display of skewness and kurtosis.

* Example generated by -dataex-. For more info, type help dataex
clear
input float y byte x float x1
-1.33 1 1
-1.41 1 1
 -1.9 1 1
  .67 2 1
  1.4 2 1
 2.09 2 1
-1.83 2 1
 -.44 1 1
  .19 2 1
 -2.2 2 1
-1.21 1 1
  .39 2 1
 -.94 1 1
 -.78 1 1
 -1.8 2 1
 1.69 1 1
  .24 2 1
 -.86 1 1
  .33 1 1
 -.57 1 1
-1.63 2 1
 2.61 2 1
  1.2 2 1
  .08 2 1
  .11 2 1
 -.22 2 1
-3.69 1 1
-1.43 1 1
  1.4 1 1
  .96 2 1
  .68 1 1
 -.17 2 1
  -.7 1 1
-1.06 2 1
  .84 1 1
-1.93 2 1
  .81 1 1
 1.91 1 1
-1.13 1 1
  .08 2 2
-1.31 1 2
 -.15 2 2
  .21 2 2
-2.45 1 2
-1.08 2 2
 5.88 2 2
  .11 2 2
 1.34 2 2
 -.02 1 2
-2.16 1 2
  .19 1 2
 1.98 2 2
 2.58 1 2
 2.13 1 2
-2.08 2 2
    0 1 2
  4.1 1 2
-2.86 2 2
-2.49 2 2
-2.07 1 2
 -2.4 2 2
-1.86 1 2
-1.95 1 2
  .95 1 2
 -.51 2 2
-2.13 2 2
-1.86 1 2
 -.41 1 2
 -4.2 1 2
-1.99 1 2
  .14 2 1
 -.98 1 1
   -2 2 1
 -.99 2 1
 5.49 1 1
  -.8 1 1
 1.29 1 1
 -.65 2 1
-1.42 1 1
-1.06 2 1
-1.67 2 1
  .96 1 1
-1.33 2 1
 -2.4 1 1
  .04 2 1
 -.97 2 1
 -.49 2 1
 1.05 1 1
-1.64 2 1
  1.6 2 1
  .13 2 1
 -1.2 2 1
-2.51 2 1
  .27 1 1
 -.83 2 1
-1.26 2 1
-1.09 1 1
  .32 2 1
-3.37 2 1
-1.52 2 1
end

egen skew = skew(y), by(x1)
egen kurt = kurt(y), by(x1)

gen toshow = "skew = " + strofreal(skew, "%3.2f") + ", kurt = " + strofreal(kurt, "%3.2f") 

gen wherey = 6
gen wherex = 0.5
qplot y, by(x1, legend(off)) trscale(invnormal(@)) yla(-5/5) addplot(scatter wherey wherex, ms(none) mlabel(toshow) mlabpos(0) mlabsize(medium) )