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首页> 外文期刊>Journal of applied statistics >On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts
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On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

机译：相关F变量的线性倒数复合分布及其在组合预测中的应用

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摘要

This paper establishes a sampling theory for an inverted linear combination of two dependent F-variates. It is found that the random variable is approximately expressible in terms of a mixture of weighted beta distributions. Operational results, including rth-order raw moments and critical values of the density are subsequently obtained by using the Pearson Type Ⅰ approximation technique. As a contribution to the probability theory, our findings extend Lee & Hu's (1996) recent investigation on the distribution of the linear compound of two independent F-variates. In terms of relevant applied works, our results refine Dickinson's (1973) inquiry on the distribution of the optimal combining weights estimates based on combining two independent rival forecasts, and provide a further advancement to the general case of combining three independent competing forecasts. Accordingly, our conclusions give a new perception of constructing the confidence intervals for the optimal combining weights estimates studied in the literature of the linear combination of forecasts.
机译：本文建立了两个相关F变量的反向线性组合的采样理论。发现随机变量在加权β分布的混合方面近似可表示。随后使用PearsonⅠ型逼近技术获得了包括r阶原始矩和密度的临界值在内的运算结果。作为对概率论的贡献，我们的发现扩展了Lee＆Hu（1996）最近对两个独立F变量线性化合物分布的研究。在相关的应用工作方面，我们的结果完善了Dickinson（1973）对基于两个独立竞争对手的预测合并的最优合并权重估计分布的询问，并为合并三个独立竞争对手的预测的一般情况提供了进一步的改进。因此，我们的结论为构建预测线性组合文献中研究的最佳组合权重估计的置信区间提供了新的认识。

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