Switching record and order statistics via random contractions

In this paper, we investigate a random contraction scheme proposed by Wesolowski and Ahsanullah (2004. Austral. NZ J. Statist. 46, 297-303). Random contraction is used in the record and order statistics settings. Some distributional recurrence relations were found for the probability density functions and distribution functions of record and order statistics. These recurrence relations lead to new characterizations of some distributions. Our results are extensions of works by Pakes (1992. Austral. J. Statist. 34, 323-339), Wesolowski and Ahsanullah (2004. Austral. NZ J. Statist. 46, 297-303) and Alzaid and Ahsanullah (2003. Comm. Statist. Theory Methods 32, 2101-2108). Some new characterizations for the Weibull and Pareto distributions and one special distribution are provided in this study.