Given the use of multiplicative cascades for the construction of multifractal measures, combined with the difficulty of obtaining the probability distribution function of a cascade generator from a realization thereof, it becomes important to develop mathematical tools to estimate the generator distributions. We are herein devising a method of obtaining the probability distribution of weights in a one-dimensional, binary multiplicative cascade, using its binary breakdown coefficients. Confirmation is provided by numerical simulations, and the method is applied to rainfall intensity time series.

中文翻译：

---

二元乘法级联中的分解系数统计

考虑到将乘法级联用于构造多重分形度量，再加上难以从级联生成器的实现中获得级联生成器的概率分布函数，开发用于估计生成器分布的数学工具就变得很重要。我们在这里设计一种使用其二进制分解系数来获得一维二进制乘法级联中权重的概率分布的方法。通过数值模拟提供了确认，并将该方法应用于降雨强度时间序列。