DISPERSION ON A SPHERE
DISPERSION ON A SPHERE
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DOI：
10.1098/rspa.1953.0064
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发表时间：
1953-01-01
影响因子：
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通讯作者：
FISHER, R
中科院分区：
文献类型：
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作者：
FISHER, R
任何拓扑学框架都需要发展一种具有特征和适当数学形式的错误理论。本文发展了一种形式的理论，似乎是适当的测量的立场上的一个领域。估计的主要问题，适用于真正的方向，和精度的意见，讨论中出现的subcases。证明了给定精度的若干随机单位向量的向量和的幅度和方向的同时分布。从这一点得出的显着性检验适用于工人的知识的精度完全在于内部证据的样本。这是高斯误差理论中的“学生”检验的类似物。所得到的一般公式用J.Hospers先生在冰岛获得的直接磁化和逆磁化熔岩流中的逆磁化方向的测量结果来说明。
Any topological framework requires the development of a theory of errors of characteristic and appropriate mathematical form. The paper develops a form of theory which appears to be appropriate to measurements of position on a sphere. The primary problems of estimation as applied to the true direction, and the precision of observations, are discussed in the subcases which arise. The simultaneous distribution of the amplitude and direction of the vector sum of a number of random unit vectors of given precision, is demonstrated. From this is derived the test of significance appropriate to a worker whose knowledge of precision lies entirely in the internal evidence of the sample. This is the analogue of ‘Student’s’ test in the Gaussian theory of errors. The general formulae obtained are illustrated using measurements of the direction of remanent magnetization in the directly and inversely magnetized lava flows obtained in Iceland by Mr J. Hospers.