The Effect of Limited Sample Sizes on the Accuracy of the Estimated Scaling Parameter for Power-Law-Distributed Solar Data
The Effect of Limited Sample Sizes on the Accuracy of the Estimated Scaling Parameter for Power-Law-Distributed Solar Data
复制标题
有限样本量对幂律分布太阳数据估计缩放参数准确性的影响
DOI：
10.1007/s11207-016-0910-5
复制
发表时间：
2016
期刊：
影响因子：
2.8
通讯作者：
S. Poedts
中科院分区：
文献类型：
--
作者：
E. D’Huys;D. Berghmans;D. Seaton;S. Poedts
许多自然过程表现出幂律行为。幂律指数与潜在的物理过程有关，因此它的精确值很有意义。例如，关于纳米耀斑的能量含量，幂律指数陡于2被认为是解决神秘的日冕加热问题的必要条件。研究几个数量级的幂律分布需要足够的数据和适当的方法。在这篇文章中，我们展示了太阳物理学中一些流行的方法，适用于典型样本量的数据的缺点。我们使用合成数据来研究样本大小对不同估计方法性能的影响。我们表明，需要大量的数据，以获得一个可靠的结果与图形的方法（幂律指数估计的对数变换的直方图上的线性拟合的数据）。我们重新审视太阳日冕物质抛射的角宽度和纳米耀斑的辐射损失的幂律公布的结果。我们证明了最大似然估计的好处，并提倡使用它。
Many natural processes exhibit a power-law behavior. The power-law exponent is linked to the underlying physical process, and therefore its precise value is of interest. With respect to the energy content of nanoflares, for example, a power-law exponent steeper than 2 is believed to be a necessary condition for solving the enigmatic coronal heating problem. Studying power-law distributions over several orders of magnitudes requires sufficient data and appropriate methodology. In this article we demonstrate the shortcomings of some popular methods in solar physics that are applied to data of typical sample sizes. We use synthetic data to study the effect of the sample size on the performance of different estimation methods. We show that vast amounts of data are needed to obtain a reliable result with graphical methods (where the power-law exponent is estimated by a linear fit on a log-transformed histogram of the data). We revisit published results on power laws for the angular width of solar coronal mass ejections and the radiative losses of nanoflares. We demonstrate the benefits of the maximum likelihood estimator and advocate its use.