In this article, a heuristic approach is used to determined the best approximate distribution of $\dfrac{Y_1}{Y_1 + Y_2}$, given that $Y_1,Y_2$ are independent, and each of $Y_1$ and $Y$ is distributed as the $\mathcal{F}$-distribution with common denominator degrees of freedom. The proposed approximate distribution is subject to graphical comparisons and distributional tests. The proposed distribution is used to derive the distribution of the elemental regression weight $\omega_E$, where $E$ is the elemental regression set.

翻译：本文采用启发式方法，在假设 $Y_1,Y_2$ 独立且每个 $Y_1$ 和 $Y$ 服从具有相同分母自由度的 $\mathcal{F}$ 分布的前提下，确定 $\dfrac{Y_1}{Y_1 + Y_2}$ 的最佳近似分布。所提出的近似分布经过图形比较和分布检验。该分布被用于推导元素回归权重 $\omega_E$ 的分布，其中 $E$ 为元素回归集。