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：我们对Ben-Akiva和Lerman(1985年)关于嵌套登录模型随机实用表示的长期推测给出了两线证据,从而对这一模型提供了更新和直截了当的教科书处理方法。 作为应用程序,我们为两个Fr\'echet随机变数与一个 Gumbel 相伴的甘贝尔相配变量之间的相互关系提供了一个封闭式公式。