Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
@did do we assume that each value has a 25% probability of occurence? thanks – ChuckM Oct 2 '12 at 6:31
Wikipedia gives 10 different ways of estimating the quantiles – Henry Oct 2 '12 at 7:36
ok I now I see what should be the correct way – ChuckM Oct 2 '12 at 8:08
thanks @did. how can I approve your answer? – ChuckM Oct 2 '12 at 19:16
up vote 0 down vote accepted

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.