We give a two-line proof of a long-standing conjecture of Ben-Akiva and Lerman (1985) 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 Fr\'echet random variables coupled by a Gumbel copula.

翻译：我们给出了Ben-Akiva和Lerman（1985）关于嵌套logit模型随机效用表示的一个长期未解猜想的双行证明，从而为该模型提供了全新且简洁的教科书式处理方法。作为应用，我们给出了由Gumbel copula耦合的两个Fr\'echet随机变量之间相关性的闭式公式。