Comparing the extremes order statistics between two random variables sequences using transmuted distributions

Luigi-Ionut Catana and Vasile Preda

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 24, 8499-8516

Abstract: This article presents new theoretical results regarding order statistics between sequences of random variables, by using several transmuted distribution families. We prove that different orders between parameters vectors imply the hazard order and reverse hazard order between extremes order statistics. The first results obtained refer to quadratic transmuted distributions. A counterexample shows that none of the orders in sense 1 or 2 is a sufficient condition for the likelihood ratio order between the corresponding smallest order statistics of two distributions. We prove that it does not exist a real distribution H such that the order in sense 1 or 2 implies the hazard rate order in the cubic transmuted distributions with one parameter. We obtain results regarding the order between parameters vectors and stochastic order of general transmuted distributions. Also, results for integrated general transmuted distributions with k parameters are given. The proofs of the results use the monotonicity, convex and Schur-convex properties. Smallest and highest order statistics are used in parallel and series systems.

Date: 2022
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DOI: 10.1080/03610926.2021.1898641

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