ON COMPOUND MULTINOMIAL DISTRIBUTION, MULTIVARIATE BETA-DISTRIBUTION, AND CORRELATIONS AMONG PROPORTIONS
ON COMPOUND MULTINOMIAL DISTRIBUTION, MULTIVARIATE BETA-DISTRIBUTION, AND CORRELATIONS AMONG PROPORTIONS
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DOI：
10.1093/biomet/49.1-2.65
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发表时间：
1962-01-01
期刊：
影响因子：
2.7
通讯作者：
MOSIMANN, JE
中科院分区：
文献类型：
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作者：
MOSIMANN, JE
自从皮尔逊（Pearson, 1897）发表了关于虚假相关性的论文以来，统计学家和生物学家都对比例或百分比之间存在的相关性持谨慎态度。然而，在许多情况下，研究人员对相关比例而不是数字直接感兴趣。也许在更多的情况下，他被迫研究比例，因为在测量实际数字方面存在巨大的实际困难。这里所描述的复合多项分布和多元l-分布提供了一种方法来确定相关性的那一部分，这只是由于比例的关系。因此，它们为解释这种性质的相关性提供了基础。复合二项分布在各种情况下都出现过。Polya（1931）根据一个瓮问题得到了这个分布。Skellam（1948）简明地推导了分布，讨论了矩和最大似然估计，并展示了其在应用中的应用。达尔文（1960）使用复合二项分布作为出发点，得到了两个分布，都称为b分布，用于研究物种频率数据。Gart（1958）在研究生存曲线时得到了复合二项分布。本文由四个部分组成。第一部分以类似于斯凯勒姆对复合二项分布的发展的方式来处理复合多项分布。第二部分给出了多项分布复利的一般结果。第三部分讨论了复利多项式分布的性质，即多元l-分布。最后，在第四节给出了前几节结果的两个生物学应用。
Statisticians and biologists alike have been wary of correlations existing among proportions or percentages since Pearson's (1897) paper on spurious correlations. Yet in many cases the research worker is directly interested in correlating proportions rather than numbers. Perhaps in even more cases he is forced to study proportions because of overwhelming practical difficulties in measuring actual numbers. The compound multinomial distribution and the multivariate fl-distribution described here afford a means of determining that portion of the correlation due only to the fact that proportions are involved. They thus provide a basis for interpretation of correlations of this nature. The compound binomial distribution has arisen in various contexts. Polya (1931) obtained the distribution as the consequence of an urn problem. Skellam (1948) concisely derived the distribution, discussed moment and maximum likelihood estimation, and showed its use in applications. Darwin (1960) used the compound binomial distribution as a point of departure in obtaining two distributions, both called the B-distribution, for studying species-frequency data. Gart (1958) obtained the compound binomial distribution in studying survival curves.This paper consists of four sections. The first treats of the compound multinomial distribution in a manner paralleling Skellam's development of the compound binomial distribution. In the second some general results in compounding the multinomial distribution are presented. In the third are discussed properties of the distribution used in compounding the multinomial, the multivariate fl-distribution. Finally, in the fourth section two biological applications of the results of the preceding sections are given.