Inequalities and the Concept of Expansions

In order to obtain rough estimates of probabilities of certain events which involve order statistics, we shall apply exponential bound theorems. These bounds correspond to those for sums of independent r.v.’s. In Section 3.1 such bounds are established in the particular case of order statistics of i.i.d. random variables with common uniform d.f. on (0,1). This section also contains two applications to moments of order statistics.