Handbook of the Logistic Distribution
Handbook of the Logistic Distribution
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DOI：
10.1080/00401706.1993.10485066
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发表时间：
1993-05
期刊：
影响因子：
2.5
通讯作者：
J. Glosup
中科院分区：
文献类型：
--
作者：
J. Glosup
这本书涵盖了逻辑分布的理论和方法以及它的一些单变量和多变量的概括。所涵盖的一些主题是估计的位置和规模参数的逻辑分布，性质和分布的顺序统计的样本从逻辑分布，以及一些应用的逻辑分布在统计，生物学和社会科学。正文不包含任何练习，但它确实提供了一些数值例子。这本书的既定目标是巩固经典和最近的结果的逻辑分布到一个单一的卷，并提供一个全面的参考书目的主题，同时提出一些新的结果。目标受众是统计学和精算学的研究生和研究人员。熟悉概率论的假设，和一些基本知识的逻辑分布及其性质似乎是预期的。由于这本书只粗略地介绍了逻辑分布，我建议不熟悉逻辑分布及其用途的读者在阅读本书之前先阅读约翰逊和科茨（1970）在本书第22章中给出的介绍。这本书分为18章，每一章都是由33位作者中的一位或几位作者撰写的。这些章节是相互独立的，可以不按顺序阅读，但第1章应先阅读。每一章都包含一个参考书目，书末提供了所有参考文献的汇编。第一章介绍了逻辑斯谛分布及其累积分布和概率密度函数。提出了几种标准化分布的方法，沿着给出了分布的前四阶矩的公式。这一章包含了所有其余章节中使用的符号和定义的描述，以及许多以前关于逻辑函数和分布的作品的列表。第2章回顾了从逻辑分布中抽取样本的顺序统计量的分布，沿着公式和关系，用于确定顺序统计量的矩、矩和累积量。结果定理和证明的形式，并扩展到适用于双删失Logistic分布的样本。也给出了许多可用于提供顺序统计量的时刻的表的列表。
This book covers the theory and methodology of the logistic distribution and some of its univariate and multivariate generalizations. Some of the topics covered are the estimation of the location and scale parameters of the logistic distribution, the properties and distributions of the order statistics of a sample from the logistic distribution, and some applications of the logistic distribution in statistics, biology, and the social sciences. The text does not contain any exercises, but it does provide a few numerical examples.The stated goal of this book is to consolidate both classical and recent results on the logistic distribution into a single volume and to provide a comprehensive bibliography to the subject while presenting some new results. The intended audience is graduate students and researchers in statistics and actuarial science. Familiarity with probability theory is assumed, and some basic knowledge of the logistic distribution and its properties seems to be expected. Since the book contains only a cursory introduction to the logistic distribution, I would recommend that readers unfamiliar with the logistic distribution and its uses read an introduction such as that given in chapter 22 of the book by Johnson and Kotz (1970) before tackling this book. The book is organized into 18 chapters, each written by one or several authors from a group of 33 contributors. The chapters are independent of one another and can be read out of order with the exception that Chapter 1 should be read first. Each chapter contains a bibliography, and a compilation of all references is provided at the end of the book. Chapter 1 contains an introduction to the logistic distribution and its cumulative-distribution and probability-density functions. Several methods for standardizing the distribution are presented, along with formulas for the first four moments of the distribution. This chapter contains descriptions of the notation and definitions used in all the remaining chapters, together with a listing of many previous works on the logistic function and distribution. Chapter 2 reviews the distributions of the order statistics for a sample taken from a logistic distribution along with formulas and relationships for determining the moments, percentiles, and cumulants of the order statistics. The results are presented in theorem and proof form and are extended to apply to samples from doubly censored logistic distributions. A listing of many of the tables available for providing moments of the order statistics is given too.