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Pareto distributions provides models for many applications in the social, natural and physical sciences. In this paper, we derive the Shannon information contained in upper (lower) k-record values and associated k-record times of Pareto-type distributions for a finite sample of fixed size and for an inverse sampling plan. Properties of the Shannon information of the k-record values associated with Pareto-type distributions are investigated, both analytically and numerically.

Generalized order statistics unify the study of order statistics, record values, k-records, Pfeifer's records and several other cases of ordered random variables. In this paper, we first provide several comparison results for generalized order statistics in terms of the dynamic cumulative residual quantile entropy order. We also prove that when the minimum of random vectors of generalized order statistics is increasing mean residual life (IMRL), the spacings of generalized order statistics are ordered by variance, and the covariance between successive spacings is nonnegative. The normalized spacings of generalized order statistics from two sample sequences are also compared with respect to the mean residual life and the excess wealth orders.

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