Introduction to Statistical Theory
Introduction to Statistical Theory
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统计理论导论
DOI：
10.1080/00401706.1972.10488997
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发表时间：
1976
影响因子：
2.8
通讯作者：
K. M. L. Suxena
中科院分区：
文献类型：
--
作者：
K. M. L. Suxena
这本书是第一个三卷系列的概率，统计和随机过程的作者写的和出版的霍顿米夫林公司根据作者，这是打算“作为一个文本的一个季度或一个学期的课程概率在juniorsenior水平”，和“材料的目的是给读者充分的准备，无论是在统计学课程或进一步研究概率论和随机过程”（序言，第vii页）。本书共分九章，每章有大量例题和平均40道习题。附标准正态概率表和指数。没有参考文献。前四章和最后一章的书处理概率空间，组合分析，离散随机变量和他们的期望，随机游走和泊松过程。这些章节写得很好。作者给出了很好的动机;定义和定理陈述清楚;例子恰当，并有效地引入了一些特殊的离散分布作为例子。第5-8章讨论连续随机变量及其期望矩母函数、特征函数、中心极限定理和弱大数定律。介绍了几种连续分布。密度的学生'st，卡方和F变量的推导（但他们的表是在第二卷，而不是本卷）。在观众的意见，这部分的书本来可以更好地组织，声明和证明的中央极限定理和弱大数定律可能出现在同一章，和大量的第6章可能出现在第二卷，而不是目前的卷。这样，它就可以为其他一些没有涉及的主题腾出空间，例如马尔可夫链的介绍，复合分布和随机数变量之和的期望（后者在第4章的练习35和第9章的9.1节中简要提及）。除了@用于正态cdf和概率生成函数，9用于正态pdf和特征函数以及其他几个目的之外，通篇使用的符号是一致的（第86页，第100页）。119-120，p. 229）。除了那些需要证明的练习外，所有的练习都有答案;有些答案是非常详细的。这可能会导致问题，因为学生可能只是简单地复制这些练习时分配的答案。
This book is the first of a three-volume series in probability, statistics and stochastic processes written by the authors and published by Houghton Mifflin Co. According to the authors, it is intended “to serve as a text for a one-quarter or one-semester course in probability at the juniorsenior level”, and “the material has been designed to give the reader adequate preparation for either a course in statistics or further study in probability theory and stochastic processes”(Preface, p. vii). The book contains nine chapters, a number of examples and an average number of 40 exercises in each chapter. Table of standard normal probabilities and index are attached. No references are given.The first four chapters and the last chapter of the book deal with probability spaces, combinatorial analysis, discrete random variables and their expectations, random walks and Poisson processes. Those chapters are very well written. The authors give good motivation; the definitions and theorems are stated clearly; the examples are appropriate and some special discrete distributions are introduced as examples effectively. Chapters 5-8 deal with continuous random variables and their expectation moment generating functions, characteristic functions, Central Limit Theorem and Weak Law of Large Numbers. Some continuous distributions are introduced. Densities of Student’st, chi-square and F variables are derived (but their tables are given in Volume II instead of the present volume). In the viewer’s opinion, this portion of the book could have been better organized, the statements and the proofs of the Central Limit Theorem and the Weak Law of Large Numbers could have appeared in the same chapter, and a great dealof Chapter 6 could have appeared in Volume II instead of the present volume. This way it would make room for some other topics which are not covered, like introduction to Markov Chains, compound distributions and expections of sums of a random number of variables (the later was touched briefly in Exercise 35, Chapter 4 and Section 9.1 of Chapter 9). Notations used throughout are consistent except@ is used for both the normal cdf and the probability generating function, 9 is used for both the normal pdf and the characteristic function and several other purposes (p. 86, pp. 119-120, p. 229). Answers to all the exercises except those which require proofs are given; some of the answers are in very detailed form. This might cause problems because students might simply copy the answers when those exercises are assigned.