Variational series
In statistics, a variational series is a non-decreasing sequence composed from an initial series of independent and identically distributed random variables. The members of the variational series form order statistics, which form the basis for nonparametric statistical methods.
is called the kth order statistic, while the values and are referred to as the extremal terms. The sample range is given by, and the sample median by when is odd and when is even.
The variational series serves to construct the empirical distribution function , where is the number of members of the series which are less than. The empirical distribution serves as an estimate of the true distribution of the random variables, and according to the Glivenko–Cantelli theorem converges almost surely to.
