Fitting a Normal Distribution to Interval and Fuzzy Data

G. Xiang, V. Kreinovich, S. Ferson
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引用次数: 2

Abstract

In traditional statistical analysis, if we know that the distribution is normal, then the most popular way to estimate its mean a and standard deviation sigma from the data sample x1,..., xn is to equate a and sigma to the arithmetic mean and sample standard deviation of this sample. After this equation, we get the cumulative distribution function F(x) = phi (x-a/sigma) of the desired distribution. In many practical situations, we only know intervals [xi, xi] that contain the actual (unknown) values of xi or, more generally, a fuzzy number that describes xt. Different values of xt lead, in general, to different values of F(x). In this paper, we show how to compute, for every x, the resulting interval [F_(x),F(x)] of possible values of F(x) -or the corresponding fuzzy numbers.
区间和模糊数据的正态分布拟合
在传统的统计分析中,如果我们知道分布是正态分布,那么最常用的方法是从数据样本x1中估计其均值a和标准差sigma,…, xn等于a和等于该样本的算术平均值和样本标准差。在这个方程之后,我们得到期望分布的累积分布函数F(x) = (x-a/sigma)。在许多实际情况下,我们只知道区间[xi, xi]包含xi的实际(未知)值,或者更一般地说,包含描述xt的模糊数。通常,不同的xt值导致不同的F(x)值。在本文中,我们展示了如何计算,对于每一个x, F(x)的可能值的结果区间[F_(x),F(x)] -或相应的模糊数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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