In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

中文翻译：

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关于嵌套LOGIT模型的表示

在本文中，我们给出了 Ben-Akiva 在 1973 年博士论文中关于嵌套 logit 模型的随机效用表示的长期猜想的两行证明，从而为该模型提供了一种更新且直接的教科书处理。作为一个应用程序，我们为通过 Gumbel copula 耦合的两个 Fréchet 随机变量之间的相关性提供了一个封闭式公式。