A nonparametric test for stop‐loss order

Abstract The increasing convex order or stop‐loss order has played a significant role in various applications within actuarial science, finance, reliability, and economics. Specifically, it has been instrumental in the comparison of risks, optimal reinsurance design, capital allocation to risk assets, optimal allocation of deductibles and coverage limits, optimal retention of stop‐loss reinsurance, and risk‐reducing investments. This article introduces a novel two‐sample nonparametric test based on two independent samples for comparing two distributions with respect to the stop‐loss order. This test provides a method for comparing the expected losses incurred above some threshold or deductible for a set of risks based on independent samples. We have developed a computational technique to evaluate the proposed test statistic, ensuring its practical applicability. Our proposed test can handle variations in sample sizes and the intersection of stop‐loss functions. To assess the performance of the test statistic, a comprehensive simulation study is conducted. Additionally, the test is applied to real‐world datasets, providing practical illustrations of its utility.