ON THE DISTRIBUTION OF THE RATIO OF THE iTH OBSERVATION' IN AN ORDERED SAMPLE FROM A NORMAL POPULATION TO AN INDEPENDENT ESTIMATE OF THE STANDARD DEVIATION
ON THE DISTRIBUTION OF THE RATIO OF THE iTH OBSERVATION' IN AN ORDERED SAMPLE FROM A NORMAL POPULATION TO AN INDEPENDENT ESTIMATE OF THE STANDARD DEVIATION
复制标题
正常总体有序样本中“iTH观测值”与标准差独立估计值之比的分布
DOI：
10.1214/aoms/1177728724
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发表时间：
1954
影响因子：
--
通讯作者：
K. V. Ramachandran
中科院分区：
文献类型：
--
作者：
K. Pillai;K. V. Ramachandran
1。摘要。本文介绍了从均值零和单位标准偏差的正常种群的尺寸为n的有序样本中的任何观察XI的分布。该分布已被开发为一系列伽马函数，并已用于获得Qi =（Xels）的分布，其中S是对自由度v的标准偏差的独立估计。以类似的方式，学生最大模量U的分布。 = i xe/s i已获得，并给出了QN的上下5％，上下给出了联合国的上和下5％。获得不同分布的方法基本上取决于正常概率积分的适当扩展及其在x和0到x的间隔中的幂。
1. Summary. This paper deals with the distribution of any observation, xi, in an ordered sample of size n from a normal population with zero mean and unit standard deviation. The distribution has been developed as a series of Gamma functions, and has been used to obtain the distribution of qi = (xels), where s is an independent estimate of the standard deviation with v degrees of freedom. In a similar manner the distribution of the Studentized maximum modulus u. = I xe/s I has been obtained and upper 5 per cent points of qn and upper and lower 5 per cent points of un have been given. The method of obtaining the different distributions essentially depends on appropriate expansions of the normal probability integral and its powers in the intervals - oo to x and 0 to x.