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Is it possible to draw the CDF of the empirical measure $\hat{P}_x$ for a i.i.d. sample realizations where $X_1 = 0.3$,$X_2 = 5$,$X_3 = 1.5$, $X_4 = 3.4$ without knowing the distribution?

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  • $\begingroup$ @did do we assume that each value has a 25% probability of occurence? thanks $\endgroup$
    – ChuckM
    Commented Oct 2, 2012 at 6:31
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    $\begingroup$ Wikipedia gives 10 different ways of estimating the quantiles $\endgroup$
    – Henry
    Commented Oct 2, 2012 at 7:36
  • $\begingroup$ ok I now I see what should be the correct way $\endgroup$
    – ChuckM
    Commented Oct 2, 2012 at 8:08
  • $\begingroup$ thanks @did. how can I approve your answer? $\endgroup$
    – ChuckM
    Commented Oct 2, 2012 at 19:16

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Yes: the empirical CDF depends only on the sample (this is what empirical refers to), here the set of values 0.3, 5, 1.5, 3.4. Even the order in which these values appeared is lost in the empirical CDF.

do we assume that each value has a 25% probability of occurence?

The empirical distribution puts mass k/n on each value, where k is the number of times said value appeared in the sample of size n. In your case, n=4 and the values are all different hence yes, each gets a weight 1/4.

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