对高斯分布参数的探究
首发时间:2017-09-30
摘要:高斯分布的两个参数锁定它具有对称的显著特征,由此决定了它固有的局限性。对称,两个参数间接相关,否则毫不相关。近似正态分布趋于非对称使其两个参数互不相关。不论对称与否若要精确地描述实际的分布形态,需要对两个参数进行深入的探究。根据高斯最原始的思路和范剑青关于分部描述降低统计误差的新理念,明确离散参数与平均值无关,以期望值为中心分解左右两个离散特征参数以计算分布曲线两侧的拐点。目的是:建立一个既能描述正态分布又能描述偏斜分布的数学模型,从而计算偏斜分布任意区间的概率,进而揭示统计对象本质的数字特征和分布规律,最终为数据的统计分析提供有效的工具和方法。达到改变传统旧观念促进推广应用之目的。
关键词: 位置特征参数 离散特征参数 正态分布 偏斜分布 高斯新分布
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Research on the Parameters of Gaussian Distribution
Abstract:The two parameters of Gaussian distribution lock it with the characteristic of symmetry, which determines its inherent limitation. Symmetry, the two parameters are indirectly related, otherwise irrelevant. The approximate normal distribution tends to be asymmetrical and makes its two parameters irrelevant. Whether symmetrical or not, it is necessary to carry out in-depth study of two parameters in order to accurately describe the actual distribution pattern. According to Gauss\'s original ideas and Fan Jianqing about the new idea of segment description reduces the statistical error, clear discrete parameters and the average value of independent, based on expectations for the center about two decomposition characteristic parameters to calculate the discrete distribution curve on both sides of the inflection point. The purpose is: to create a can not only describe the normal distribution but also describe skewed distribution, the mathematical model to calculate arbitrary skew distribution interval probability, which demonstrates the nature of statistical object digital characteristics and distribution, finally provide effective tools for statistical analysis of data and methods. Achieve the purpose of changing traditional old ideas and Promoting Popularization and application.
Keywords: position characteristic parameter discrete characteristic parameter;normal distribution skew distribution Gauss new distribution
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