概率n-单形上均匀分布的随机向量的最大坐标的矩和危险率阶的限制性
The restrictiveness of the hazard rate order and the moments of the maximal coordinate of a random vector uniformly distributed on the probability n-simplex
摘要：
在文[9]中定义了随机序的限制性，并计算了一般随机序和似然比序的限制性的基础上，我们计算了风险率序的限制性。受[17]和[24]工作的启发，我们提出了限制性结果在随机性检验中的一个可能的应用。然后，我们应用降维技术，证明有用的限制性的结果，并提供了一个替代证明惠特沃思公式。通过对公式的积分，我们导出了均匀分布在概率$n$ -单形上的随机向量的最大坐标的矩。
英文摘要：
Continuing the work of [9] who defined the restrictiveness of stochastic orders and calculated the restrictiveness of the usual stochastic order and the likelihood ratio order, we calculate the restrictiveness of the hazard rate order. Inspired by the works of [17] and [24], we propose a possible application of the restrictiveness results in randomness testing. We then apply a dimension reduction technique, that proved useful in obtaining the restrictiveness results, and provide an alternative proof for Whitworth's formula. By integrating the formula, we derive the moments of the maximal coordinate of a random vector that is uniformly distributed on the probability $n$-simplex.
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