quantile vs ecdf results

Question

I am trying to use ecdf, but I am not sure if I am doing it right. My ultimate purpose is to find what quantile corresponds to a specific value. As an example:

sample_set <- c(20, 40, 60, 80, 100) 
# Now I want to get the 0.75 quantile:
quantile(x = sample_set, probs = 0.75)
#result:
75% 
80
# Let's use ecdf
ecdf(x = sample_set) (80)
#result
0.8

Why is there this discrepancy? Am I doing some trivial mistake, or it depends on the way quantile makes its calculations?

Thanks, Max

Maybe the calculations would make more sense if you looked at `plot(ecdf(x = sample_set)); abline(h = 0.75,col = "blue")`? Certainly one (or both) of those directions is ambiguous...? — joran, Mar 10 '16 at 22:05

Julius Vainora · Accepted Answer · 2016-03-10T22:19:38.147

5

There are two points. First, as you guessed, it depends on the way quantile makes its calculations. Specifically, it depends on the parameter type. What you might want to choose is type = 1, since then it corresponds to the inverse of empirical distribution function (see ?quantile). Second, since ecdf gives a discrete, step function, i.e. the ecdf is not strictly increasing, you cannot get exact equality because of the way quantile is defined (see the second formula).

edited Mar 10 '16 at 22:19

answered Mar 10 '16 at 22:05

Julius Vainora

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I assume you mean the ecdf is not *strictly* increasing. Its an increasing function in the often used sense of monotonic non-decreasing. – A. Webb Mar 10 '16 at 22:10
@A.Webb, yes, that is what I meant. I will add this word to avoid confusion. – Julius Vainora Mar 10 '16 at 22:19

quantile vs ecdf results

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