This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN in many disparate phenomena. Here, I characterize its PDF, CDF, moments, and parameter estimators; generalize it to N-dimensions using spherical distribution theory; describe methods to deal with its signature ``double-exponential'' nature; and use it to generalize growth measurement to possibly-negative variates distributing DLN. I also conduct Monte-Carlo experiments to establish some properties of the estimators and measures described.

翻译：本文描述了对数正态差（DLN）分布。配套论文论证了DLN是自然界中的基本分布，并展示了中心极限定理的简单应用如何在许多不同现象中产生DLN。在此，我刻画了其概率密度函数、累积分布函数、矩及参数估计量；利用球面分布理论将其推广至N维空间；描述了处理其标志性"双指数"特性的方法；并将其应用于增长测量，使其适用于服从DLN的可能为负的变量。我还进行了蒙特卡洛实验，以建立所述估计量与度量的一些性质。