On recursive computation for the moments of generalized order statistics for the Kumaraswamy family of distributions with characterizations

The generalized order statistics (GOS) is a unified model for random variables that are arranged in increasing order of magnitude. Several other models for increasingly arranged random variables appear as special cases of GOS. The distributional properties of generalized order statistics for specific baseline distributions have been studied by various authors. One specific domain of study in the context of generalized order statistics is to develop some recursive formulae to obtain moments of the distribution of generalized order statistics for any baseline distribution. The relations for the moments of generalized order statistics for families of distributions have not been explored much. This paper is based on some recursive relations to compute the single and joint moments of generalized order statistics for the Kumaraswamy family of distributions. These relations are useful to recursively compute the single and joint moments of generalized order statistics for any member of the Kumaraswamy family of distributions. We illustrate the results with examples using different baseline distributions. Additionally, we present some characterization results using single and joint moments of GOS.