Dispersive and Star Orders on Extreme Order Statistics from Location-Scale Samples

Order statistics are of significant importance in various fields, including reliability, auctions, and actuarial science. This paper explores the stochastic orderings of extreme order statistics within the location-scale samples. Our findings demonstrate that the stochastic orderings of extreme order statistics is independent of the location parameter and is influenced solely by the scale parameter. Meanwhile, we further establish the conditions under which the scale parameter induces dispersive order and star order on the maximum order statistic, and provide sufficient conditions for these orders to hold for the minimum order statistic. Finally, Numerical examples are presented to validate the effectiveness of the theoretical findings.