Probability, Random Variables, and Stochastic Processes
Probability, Random Variables, and Stochastic Processes
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DOI：
10.1080/00401706.1966.10490365
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发表时间：
1966-05
期刊：
影响因子：
2.5
通讯作者：
I. Miller
中科院分区：
文献类型：
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作者：
I. Miller
在上述任何一项中，作者都没有确定除了El之外所涉及的统计分布。作者显然不打算将他的听众限于统计人员;因此，上述批评主要对这一群体是有效的。然而，更普遍（但较小）的批评是：（1）缺乏对可用于评估某些多元正态概率的表格的讨论，例如DB Owen的统计表手册（Addison-Wesley，1962）;（2）未能提供渐近（即，中心极限）结果，这产生了多元正态分布;（3）缺乏对“正态”二次型分布的讨论，这在线性模型分析中很重要。作为这本书的先决条件，作者假设“读者熟悉有关线性代数的基本事实，并对高等微积分和概率论有一定的了解。”此外，对于读者谁打算做更多的调查的内容，背景涵盖特殊函数理论，特别是超几何函数及其特殊情况，将是可取的。或者，读者可能希望通过填写或检查文本中提供的材料来沿着这些线路发展他的知识。总之，这本书提供了一个发展的多元正态分布的水平需要知识的理论概率，矩阵，和特殊功能。主要的不足，从统计的观点来看，是缺乏一定的方向，但尽管这种批评，这是一个显着的除了少数书籍提供的理论多元分析。
In none of the above does the author identify the statistical distribution involved except in El. The author apparently did not intend to restrict his audience to statisticians; hence, the foregoing criticisms are valid primarily with respect to this group. More general (but minor) criticisms, however, are:(1) the lack of a discussion of tables available for evaluating certain multivariate normal probabilities, such as are available in DB Owen’s Handbook of Statistical Tables (Addison-Wesley, 1962);(2) the failure to present asymptotic (ie, central limit) results, which produce the multivariate normal distribution; and (3) the lack of a discussion of distributions of “normal” quadratic forms, important in linear model analysis. As prerequisit, es for this book, the author assumes “the reader is familiar with the elementary facts concerning linear algebra and has some acquaintance with advanced calculus and probability theory.” Additionally, for the reader who intends to do more than survey the contents, background covering special function theory, particularly the hypergeometric function and it, s special cases, would be desirable. Alternatively, the reader may wish to develop his knowledge along these lines by filling in or checking out material presented in the text. In summary, the book provides a development of the multivariate normal distribution at a level requiring knowledge of the theory of probability, matrices, and special functions. The main deficiency, from a statistical viewpoint, is a certain lack of orientation, but despite this criticism, it is a significant addition to the small number of books available on the theory of multivariate analysis.