MATLAB: Does the ecdf function return duplicate x values

cumulative distributionecdfStatistics and Machine Learning Toolbox

When calling the ecdf function (empirical cumulative distribution function), why is the first "x" value always duplicated? This means that the first 'F' output is always 0. For example:
 Trial>> y = 0:10;
 Trial>> [f,x] = ecdf( y );
 Trial>> disp(x')
      0     0     1     2     3     4     5     6     7     8     9    10
 Trial>> y = 5:15;
 Trial>> [f,x] = ecdf( y );
 Trial>> disp(x')
      5     5     6     7     8     9    10    11    12    13    14    15
In other words, the minimum value in the input array always appears twice, but the corresponding F value in the first instance is always 0. Since the ECDF is given by:
…is this correct?
Thanks!

Best Answer

This is just for convenience in plotting. Compare these:
>> y = rand(10,1);
>> [f,x] = ecdf(y);
>> subplot(2,1,1); stairs(x,f)
>> subplot(2,1,2); stairs(x(2:end),f(2:end))
Your formula is correct. If you need only the values after each jump in the cdf, you can discard the first value from both x and f.
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