Asymptotic fisher information in order statistics of geometric distribution

In this paper, the geometric distribution is considered. The means, variances, and covariances of its order statistics are derived. The Fisher information in any set of order statistics in any distribution can be represented as a sum of Fisher information in at most two order statistics. It is shown that, for the geometric distribution, it can be further simplified to a sum of Fisher information in a single order statistic. Then, we derived the asymptotic Fisher information in any set of order statistics.