The Empirical Distribution Function and the Histogram

Note that this is simply the distribution function of a discrete random variable that places mass 1/n in the points X1, . . . , Xn (provided all these are distinct). Note also that one can also define the empirical probability of any Borel-measurable set B as Pn(B) = 1 n ∑n i=1 1{Xi ∈ B}. Note that the order of the samples is not important in the computation of Fn. For that reason it is useful to define the order statistics.