Laguerre Polynomials in Production Simulation

这项研究旨在为解决这一问题提供一种新颖的方法， 电力系统的生产成本。 当前思维的核心 与生产成本计算相关的是“累积量”概念。 或概率分布一阶矩近似。 这些 卷积计算可能是令人烦恼的，因为已知它们非常 在决策过程中准确和严重误导时有用 不准确的时候。 有限范围的分布总是可以 以它的所有时刻为特征。 近似值需要几个 但有多少是个问题。 标准近似值为 累积量是Gram-Charlier级数及其Hermite多项式。 有初步证据表明，这一系列是根源， 问题和正交级数如Laguerre多项式 扩张提供了解决方案。 这项工作将在悉尼进行， 澳大利亚在新南威尔士大学，因为，在 根据PI的建议，工作已经开始。 我预计 答案是这项工作的结果，并为今后的工作提供专门知识 居住在俄亥俄州大学。

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.