Generalized moments of sample extremes of order statistics from discrete uniform distribution

Moments of order statistics in continuous random variables can be found easily. In contrast, since distributions of order statistics are more complex in discrete case, it is not easy to find their moments. Some specific approaches have been put forward for calculating these moments. Moments of order statistics of some discrete distributions can be calculated by using these approaches.In the first chapter of this study, the histories of order statistics and developments in this field up to now have been related. In the second chapter, some concepts, features and approaches are given. With the help of the given approaches, moments of maximum and minimum order statistics in discrete uniform distributions are generalized by using beta integral form. Additionally, expected values and variances of the sample extremes of order statistics in discrete uniform distributions are calculated numerically and they are given in a table.