非正态分布的测量误差和行差限值的讨论
On the measuring errors of non-normal distribution and the limits of run error
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摘要: 测量误差中大多数是正态分布变量,但还有的是均匀分布变量,有的是服从正态分布与均匀分布之和的变量,有的是正态分布变量的函数。因此,在分析测量误差时,除要研究正态分布外,还须对其他类型的分布进行研究,本文主要讨论均匀分布与正态分布之和的分布,推演了它的分布密度和概率的计算公式。监把它和正态分布进行了比较。此外,分析了测量误差中的行差改正数,指出它是一个均匀分布变量,因此受行差影响的照准误差就不再是正态变量,而是服从二种分布之和的分布。为了使观测工作和应用观测成果方便起见,我们希望受行差影响的照准误差实际上仍可当作一个正态分布变量,为此,对行差必须规定一个限值,经分析比较,建议行差限值取2β=3σ,其中σ是照准方根差。最后对现行《规范》规定的J07,J1型经纬仪和S05型水准仪的行差限值提出了修正的意见。Abstract: Besides the normal distribution errors,there are other varieties of measuring errors,such as,the uniform distribution errors or the errors subjected to the distribution of the sum of a uniform distribution and a normal distribution.This paper is intended mainly to discuss the distribution of the sum of a uniform distribution and a normal distribution.The formulas of the distribution density and the probability of this distribution are derived and a comparison between this distribution and the normal distribution is made.Then the author analyses the sighting error of a precision theodolite or level influenced by the run error of the micrometer and points out that this error subordinates to the distribution discussed above.The limit of the run error is suggested as 2β=3σ,where σ is the standard deviation of the sighting error Finally opinions are expressed for the revision of the current official specification for the run error limit of the then dolits J07,J1 and the level S05.
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