Laguerre Polynomials in Production Simulation

本研究旨在为解决电力系统生产成本问题提供一种新颖的方法。当前有关生产成本计算的核心思想是“累积量”或概率分布第一矩近似的概念。这些卷积计算可能令人烦恼，因为它们在准确时非常有用，而在不准确的决策过程中会严重误导。有限范围的分布总是可以用它的所有矩来表示。近似需要一些时间，但问题是需要多少时间。累积量的标准近似是带有埃尔米特多项式的格拉姆-查利尔级数。有初步的证据表明，这个级数是问题的根源，而正交级数如拉盖尔多项式展开提供了解决方案。这项工作将在澳大利亚悉尼的新南威尔士大学进行，因为根据PI的建议，那里的工作已经开始了。我希望这个问题的答案是这项工作的结果，并为俄亥俄大学未来的工作提供专业知识。

This research is aimed at a fresh and novel approach to the problem of production costing in power systems. Central to current thinking relative to production cost calculation is the concept of "cummulants" or probability distribution first moment approximations. These convolution calculations can be vexing since they are known to be very useful when accurate and severely misleading in the decision process when inaccurate. A distribution of finite range can always be characterized by all of its moments. Approximations require a few moments but, how many is the question. The standard approximation to cummulants is the Gram-Charlier series with its Hermite polynomials. There is preliminary evidence that this series is the root of the problem and that orthogonal series such as Laguerre polynomial expansions offer solution. The work will be performed in Sydney, Australia at the University of New South Wales because, at the suggestion of the PI, work has already begun there. I expect the answer to be a result of this work with the expertise for future work to reside at Ohio University.