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

min

th order statistics, respectively) are referred to as the extremal terms.

[1] The sample range is given by

,[1] and the sample median by

is odd and

The variational series serves to construct the empirical distribution function

( x ) = μ ( x )

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

This statistics-related article is a stub.

You can help Wikipedia by expanding it.