In the literature of stochastic orders, one rarely finds results characterizing non-comparability of random variables. We prove simple tools implying the non-comparability with respect to the convex transform order. The criteria are used, among other applications, to provide a negative answer for a conjecture about comparability in a much broader scope than its initial statement.

中文翻译：

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凸变换阶与应用程序的不可比性

在随机顺序的文献中，很少发现表征随机变量不可比性的结果。我们证明了简单的工具暗示了凸变换阶的不可比性。在其他应用中，该标准用于为比其初始陈述更广泛的可比性猜想提供否定答案。