Example 7.11: Plot an empirical cumulative distribution function from scratch

August 31, 2009

(This article was first published on SAS and R, and kindly contributed to R-bloggers)

In example 7.8, we used built-in functions to produce an empirical CDF plot. But the empirical cumulative distribution function (CDF) is simple to calculate directly, and it might be useful to have more control over its appearance than is afforded by the direct method employed in example 7.8. In a later post, we’ll use that control to improve upon example 7.8.


In SAS, we first read the data from a locally stored Stata data set. Then, we calculate the empirical CDF for pcs. We do this by first sorting (1.5.6) on pcs. Then the order statistic of the observation divided by the total number of obervations is the empirical probability that X ≤ x. We find the number of observations using the nobs data set option (A.6.1) and the observation number using the _n_ implied variable (1.4.15). Then we can plot the empirical CDF using proc gplot (section 5.1.1) to make a scatterplot and a symbol statement with the j interpolation (as in section 1.13.5) to connect the points.

proc import datafile="C:bookhelp.dta"
out=help dbms=dta;

proc sort data=help;
by pcs;

data help_a;
set help nobs=totalobs;
ecdf_pcs = _n_ / totalobs;

symbol1 i=j v=none c=blue;
proc gplot data=help_a;
plot ecdf_pcs * pcs;

Now, R. First, make the ECDF values in a similar fashion to SAS, then make an empty frame (5.1.1), then fill the frame with lines connecting the calculated values (5.2.1).

ds <- read.dta
sortpcs <- sort(pcs)
ecdfpcs <- (1:length(sortpcs))/length(sortpcs)
plot(sortpcs, ecdfpcs, type="n")
lines(sortpcs, ecdfpcs)

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