目录

  • 1 概率论的基本概念
    • 1.1 随机试验
    • 1.2 样本空间、随机事件
    • 1.3 频率与概率
    • 1.4 等可能概型(古典概型)
    • 1.5 条件概率
    • 1.6 独立性
  • 2 随机变量及其分布
    • 2.1 随机变量
    • 2.2 离散型随机变量及其分布
    • 2.3 随机变量的分布函数
    • 2.4 连续型随机变量及其概率密度
    • 2.5 随机变量的函数的分布
  • 3 多维随机变量及其分布
    • 3.1 二维随机变量
    • 3.2 边缘分布
    • 3.3 新建目录
    • 3.4 新建目录
    • 3.5 二维随机变量的特征数
  • 4 随机变量的数字特征
    • 4.1 数学期望
    • 4.2 随机变量的数字特征
    • 4.3 协方差及相关系数
    • 4.4 矩、协方差矩阵
  • 5 大数定律与中心极限定理
    • 5.1 大数定律
    • 5.2 中心极限定理
  • 6 统计量及其分布
    • 6.1 样本数据的整理与显示
    • 6.2 统计量及其分布
  • 7 参数估计
    • 7.1 点估计得几种方法
    • 7.2 点估计的评价标准
    • 7.3 区间估计
  • 8 假设检验
    • 8.1 假设检验的基本思想与概念
    • 8.2 正态总体参数假设检验
  • 9 基于R语言的实验
    • 9.1 R语言介绍
    • 9.2 R软件下载与安装
    • 9.3 初识R软件
    • 9.4 蒲丰投针的计算
    • 9.5 同一天生日的计算
    • 9.6 抛硬币和骰子
    • 9.7 两点分布
    • 9.8 二项分布
    • 9.9 泊松分布
    • 9.10 正态分布
    • 9.11 指数分布
R语言介绍

R软件介绍

The current R is the result of a collaborative effort with contributions from all over the world. R was initially written by Robert Gentleman and Ross Ihaka—also known as “R & R” of the Statistics Department of the University of Auckland. Since mid-1997 there has been a core group, the R Core Team, with write access to the R source.

Introduction to R

R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R.

R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, …) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity.

One of R’s strengths is the ease with which well-designed publication-quality plots can be produced, including mathematical symbols and formulae where needed. Great care has been taken over the defaults for the minor design choices in graphics, but the user retains full control.

R is available as Free Software under the terms of the Free Software Foundation’s GNU General Public License in source code form. It compiles and runs on a wide variety of UNIX platforms and similar systems (including FreeBSD and Linux), Windows and MacOS.

The R environment

R is an integrated suite of software facilities for data manipulation, calculation and graphical display. It includes

  • an effective data handling and storage facility,

  • a suite of operators for calculations on arrays, in particular matrices,

  • a large, coherent, integrated collection of intermediate tools for data analysis,

  • graphical facilities for data analysis and display either on-screen or on hardcopy, and

  • a well-developed, simple and effective programming language which includes conditionals, loops, user-defined recursive functions and input and output facilities.

The term “environment” is intended to characterize it as a fully planned and coherent system, rather than an incremental accretion of very specific and inflexible tools, as is frequently the case with other data analysis software.

R, like S, is designed around a true computer language, and it allows users to add additional functionality by defining new functions. Much of the system is itself written in the R dialect of S, which makes it easy for users to follow the algorithmic choices made. For computationally-intensive tasks, C, C++ and Fortran code can be linked and called at run time. Advanced users can write C code to manipulate R objects directly.

Many users think of R as a statistics system. We prefer to think of it as an environment within which statistical techniques are implemented. R can be extended (easily) via packages. There are about eight packages supplied with the R distribution and many more are available through the CRAN family of Internet sites covering a very wide range of modern statistics.

R has its own LaTeX-like documentation format, which is used to supply comprehensive documentation, both on-line in a number of formats and in hardcopy.