Gamma和韦布尔分布下的迭代故障率单调性和序关系
Iterated failure rate monotonicity and ordering relations within Gamma and Weibull distributions
摘要：
随机变量分布的随机排序可以由尾函数的相对凸性来定义。这已经扩展到高阶随机排序，通过迭代重新分配尾部权重。这些随机排序的实际验证并不简单，因为这取决于反演分布函数，而这些分布函数可能没有明确的表达式。当然，分布的迭代定义使得验证更加困难。我们看一下随机排序，介绍一种方法，允许明确的使用，将其应用到伽玛和韦布尔分布，给出了这些家庭内的顺序关系的完整描述。
英文摘要：
Stochastic ordering of distributions of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of those stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order relations within each of those families.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
