No abstract

Abtsrcat Order statistics, record values and several other model of ordered random variables can be viewed as special case of generalized order statistics ( gos) [Kamps, 1995]. Pawlas and Szynal (2001) introduced the con-cept of lower generalized order statistics ( lgos) to enable a common approach to descending ordered rv's like reversed order statistics and lower record values. The work of Burkschat et al. (2003) may also be seen for dual (lower) generalized order statistics. In this paper simple expressions for single and product moments of lower generalized order statistics from power function distribution have been obtained. Further, some important deductions and computational works are carried out.

A general class of distribution F( x) = ah( x) + b has been characterized by considering conditional moments of a function of two order statistics, conditioned on the pair of order statistics. Further, its important consequences are also discussed.

We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

The Marshall-Olkin extended uniform distribution is introduced and studied by Jose and Krishna (2011). In this paper some moments properties of generalized order statistics (gos) for this distribution are investigated and results are deduced for order statistics and record values. In the last section, a characterization result is presented.