CONFIDENCE INTERVALS FOR COEFFICIENT OF VARIATION FOR NORMAL + LOG NORMAL DISTRIBUTIONS
CONFIDENCE INTERVALS FOR COEFFICIENT OF VARIATION FOR NORMAL + LOG NORMAL DISTRIBUTIONS
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DOI：
10.1093/biomet/51.1-2.25
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发表时间：
1964-01-01
期刊：
影响因子：
2.7
通讯作者：
ROSENBLATT, JI
中科院分区：
文献类型：
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作者：
KOOPMANS, LH;OWEN, DB;ROSENBLATT, JI
该参数提供了X相对于其平均值的变异性的无量纲度量，这在许多实际应用中是有用的。例如，见Duerst（1956）、Goodman（1953）和Weiler（1958）。Norris（1938）给出了一些比样本变异系数更好的测量某些非正态随机变量的相对离差的方法。Wijsman（1956，1958）和Glasser（1962）考虑了均值与标准差的比值。在正态性的情况下，McKay（1932）、Pearson（1932）和Fieller（1932）研究了样本变异系数分布的数值近似。当X服从正态分布时，基于大小为n的样本的r的自然估计是统计量V= s/X，其中X和s是样本均值和标准差。该估计具有吸引人的特征，即t= V具有n-1自由度的非中心Student t分布和非中心性参数a= Inljr。这个事实被约翰逊和韦尔奇利用了吗？（1940）通过获得d的置信下限d（t）来获得r的1-a置信上限。然而，即使假设a> 0，d（t）< 0的出现（因此，r的无限上限）对所有a都有正概率，并且对于接近零的a，它可以任意接近1-a。显然，这种限制很少有用。它将在？2，没有一些先验信息的范围内的参数它，它是，事实上，不可能获得的置信区间r具有有限的长度与概率为1的所有值的它和一个，除了由一个纯粹的顺序抽样计划。通过构造一个序列方案，证明了具有此性质的序列方案确实存在。t桑迪亚公司，阿尔伯克基，新墨西哥州。这些作者的工作是在原子能委员会的主持下进行的。
This parameter provides a dimensionless measure of the variability of X relative to its mean which is useful in many practical applications. For example, see Duerst (1956), Goodman (1953) and Weiler (1958). Norris (1938) gives some better measures of relative dispersion than the sample coefficient of variation for certain non-normal random variables. Wijsman (1956, 1958) and Glasser (1962) consider the ratio of mean to standard deviation. In the case of normality, McKay (1932), Pearson (1932) and Fieller (1932) have studied a numerical approximation to the distribution of the sample coefficient of variation. When X is normally distributed, the natural estimate of r based on a sample of size n is the statistic V= s/X, where X and s are the sample mean and standard deviation. This estimate has the appealing feature that t= V has the non-central Student t-distribution with n-1 degrees of freedom and non-centrality parameter a= Inljr. This fact was used by Johnson & Welch?(1940) to obtain a 1-a upper confidence limit for r by obtaining a lower confidence limit, d (t), for d. However, even assuming a> 0 as they do, the occurrence of d (t)< 0 (and, hence, of an infinite upper limit for r) has positive probability for all a and, for a near zero, it can be arbitrarily close to 1-a. Such limits are, clearly, seldom useful. It will be shown in? 2 that without some a priori information about the range of the parameter It it is, in fact, impossible to obtain confidence intervals for r which have finite length with probability one for all values of It and a, except by a purely sequential sampling scheme. That sequential schemes with this property do exist is established by constructing one. t Sandia Corporation, Albuquerque, New Mexico. Work by these authors was performed under the auspices of the Atomic Energy Commission.