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Are there any free statistical textbooks available?

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    $\begingroup$ Look at Statistics Topics ebook on Amazon by Mehta, and his free web log Statistics Ideas that has lecture slides. Nearly free and better in some pedagogical topics, than the ones you cite on your list of resources. $\endgroup$
    – user48690
    Commented Jun 20, 2014 at 0:16

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Online books include

Update: I can now add my own forecasting textbook

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The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman is a standard text for statistics and data mining, and is now free:

https://web.stanford.edu/~hastie/ElemStatLearn/

Also Available here.

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    $\begingroup$ Why pay $70 for the book? To support the authors and to have a physical copy. That's why I did it, anyway! $\endgroup$
    – Shane
    Commented Jul 23, 2010 at 17:13
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    $\begingroup$ I agree with Shane... and a hardcopy makes reading it much easier. $\endgroup$
    – Vince
    Commented Jul 24, 2010 at 0:07
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    $\begingroup$ Did that, too (previous edition). But it is nice to be able to look things up online when the book is not at hand. And to have access to the new edition. $\endgroup$
    – cbeleites
    Commented Aug 17, 2012 at 12:03
  • $\begingroup$ (+1) Just wanted to comment that this is a GREAT book, it is my all-time favorite. I also ordered a physical copy of it :-). $\endgroup$
    – Néstor
    Commented Aug 20, 2012 at 3:13
  • $\begingroup$ If you attend Hastie and Tibshirani's Statistical Learning and Data Mining seminar, you'll receive a free copy of the text. And you can have your book signed! $\endgroup$
    – RobertF
    Commented Feb 26, 2013 at 18:36
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Introduction to Statistical Thought

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    $\begingroup$ Michael Lavine is a clear lecturer and thinker, so I have little doubt his book is worth a look. $\endgroup$
    – whuber ♦
    Commented Oct 8, 2010 at 20:26
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    $\begingroup$ I'm teaching out that book this semester. It may be a good statistics book, but I'm having second thoughts regarding its light probability content. $\endgroup$
    – John D. Cook
    Commented Oct 9, 2010 at 1:21
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There's a superb Probability book here: https://web.archive.org/web/20100102085337/http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html which you can also buy in hardcopy.;

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I've often found the Engineering Statistics Handbook useful. It can be found here.

Although I've never read it myself, I hear Introduction to Probability and Statistics Using R is very good. It's a full ~400 page ebook (also available as an actual book). As a bonus, it also teaches you R, which of course you want to learn anyways.

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    $\begingroup$ +1 For this resource. As the name says, excellent for a practical approach to engineering problems. $\endgroup$
    – Bossykena
    Commented Jul 26, 2010 at 17:42
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Machine Learning

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Switching now to more specialized topics, there are:

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I really like The Little Handbook of Statistical Practice by Gerard E. Dallal

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Here's a fresh one: Introduction to Probability and Statistics Using R . It's R-specific, though, but it's a great one. I haven't read it yet, but it seems fine so far...

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Norman Matloff has written a mathematical statistics textbook for computer science students that's free. Kind of a niche market, I suppose. For what it's worth, I haven't read it, but Matloff has a Ph.D. in mathematical statistics, works for a computer science department, and wrote a really good R book, that I recommend for people who want to go to the next stage of programming R better (as opposed to just fitting models with canned functions).

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OpenIntro Statistics

http://www.openintro.org/stat/textbook.php

Inexpensive paperback copies are also available on Amazon.

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    $\begingroup$ I moved this from answer to comment since I am expressing my opinion about free books on the net rather than providing a a list of some. As both an author and owner of books I see both sides. I appreciate that most statistics books, especially when they deal with specialized topics are very expensive. However as an author who has put in a lot of effort to try to write useful and informative books I think the authors and publishers deserve remuneration for the efforts they go through to produce the books. So I don't think books should be free. $\endgroup$
    – Michael R. Chernick
    Commented Aug 17, 2012 at 21:13
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    $\begingroup$ But if authors want to put out material on the internet for free that is their choice. We all can benefit from that. $\endgroup$
    – Michael R. Chernick
    Commented Aug 17, 2012 at 21:14
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    $\begingroup$ You could make the same arguments about software, but we all benefit from R. $\endgroup$
    – Jeremy Miles
    Commented Mar 2, 2015 at 3:47
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A New View of Statistics by Will G. Hopkins is great! It is designed to help you understand how to understand the results of statistical analyses, not how to prove statistical theorems.

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"An Introduction to Statistical Learning with Applications in R" https://www.statlearning.com/ by two of the 3 authors of the well-known "The Elements of Statistical Learning" plus 2 other authors. An Introduction to Statistical Learning with Applications in R is written at a more introductory level with less mathematical background required than The Elements of Statistical Learning, makes use of R (unlike The Elements of Statistical Learning), and was first published in 2013, some years after this thread was started.

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Not Statistics specific, but a good resource is: http://www.reddit.com/r/mathbooks Also, George Cain at Georgia Tech maintains a list of freely available maths texts that includes some statistical texts. http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html

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For getting into stochastic processes and SDEs, Tom Kurtz's lecture notes are hard to beat. It starts with a decent review of probability and some convergence results, and then dives right into continuous time stochastic processes in fairly clear, comprehensible language. In general it's one of the best books on the topic -- free or otherwise -- I've found.

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I really like these two books by Daniel McFadden of Berkeley:

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Cosma Shalizi, CMUs ML guru, occasionally updates a draft of a stats book soon to be published by Cambridge Press titled Advanced Data Analysis from an Elementary Point of View. Can't recommend it highly enough...

Here's the Table of contents:

I. Regression and Its Generalizations
Regression Basics
The Truth about Linear Regression
Model Evaluation
Smoothing in Regression
Simulation
The Bootstrap
Weighting and Variance
Splines
Additive Models
Testing Regression Specifications
Logistic Regression
Generalized Linear Models and Generalized Additive Models
Classification and Regression Trees 

II. Distributions and Latent Structure
Density Estimation
Relative Distributions and Smooth Tests of Goodness-of-Fit
Principal Components Analysis
Factor Models
Nonlinear Dimensionality Reduction
Mixture Models
Graphical Models 

III. Dependent Data
Time Series
Spatial and Network Data
Simulation-Based Inference 

IV. Causal Inference
Graphical Causal Models
Identifying Causal Effects
Causal Inference from Experiments
Estimating Causal Effects
Discovering Causal Structure 

Appendices
Data-Analysis Problem Sets
Reminders from Linear Algebra
Big O and Little o Notation
Taylor Expansions
Multivariate Distributions
Algebra with Expectations and Variances
Propagation of Error, and Standard Errors for Derived Quantities
Optimization
chi-squared and the Likelihood Ratio Test
Proof of the Gauss-Markov Theorem
Rudimentary Graph Theory
Information Theory
Hypothesis Testing
Writing R Functions
Random Variable Generation
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    $\begingroup$ I point people to Cosma's notes regularly. There's some good material in there $\endgroup$
    – Glen_b
    Commented Jun 6, 2016 at 1:10
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Some free Stats textbooks are also available here.

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I know other authors have gone to some trouble to make their books available here on stack exchange ... The printed version of our 2002 edition was printed 3 times and sold out 3 times; Springer and Google recently started selling it (book only) as a PDF eBook (no software) on the Springer and Google sites for $79.

We are delighted to be able to make the PDF eBook version (2002 edition) available for FREE to stackexchange users at:

http://www.mathstatica.com/book/bookcontents.html

enter image description here

This is a complete PDF version of the original 2002 printed edition. Although no software is included (neither Mathematica nor mathStatica), the methods, theorems, summary tables, examples, exercises, theorems etc are all useful and relevant ... even as a reference text for people who do not even have Mathematica.

One can either download:

  • the entire book as a single download file ... with live clickable Table of Contents etc, ... or

  • chapter by chapter.

iBooks installation

To install as an iBook:

  • Download the entire book as a single PDF file

  • Then drag it into iBooks (under the section: PDF files).

iPad installation

To install on an iPad:

  • First install it as an iBook (as above)

  • Open iTunes; select your iPad; click on Books: select the book and sync it over to your iPad.

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It's nice to see academics freely distribute their works. Here is trove of free ML / Stats books in PDF:

Machine Learning

Probability / Stats

Linear Algebra / Optimization

Genetic Algorithm

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  • $\begingroup$ If LADW is mentioned, perhaps LADR by Axler could have been mentioned too; the latter is way better book imo. $\endgroup$
    – User1865345
    Commented Jun 2, 2023 at 12:04
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Statsoft's Electronic Statistics Handbook ('The only Internet Resource about Statistics Recommended by Encyclopedia Britannica') is worth checking out.

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  • $\begingroup$ This link now redirects to a product page for a data science/AI software. Can you update the link, if this resource is still freely available? $\endgroup$
    – dipetkov
    Commented Mar 31, 2023 at 9:07
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Not properly an entire textbook, but the part IV of Mathematics for Computer Science is about probability and random variables.

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A write up of probability tutorials and related puzzles along with R code for learning. Hope it helps

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http://www.probabilitycourse.com/ is a website hosting free online-based Probability and Statistics textbook. It also has extra features such as graphing tools and lecture videos

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Here is also a great free book on multivariate statistics by Marden, primarily concerned with the normal linear model linked on this page:

Multivariate Statistics Old School by John I. Marden

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Gelman et al. "Bayesian Data Analysis" (3rd edition).

enter image description here

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    $\begingroup$ How do I shrink the picture? :) $\endgroup$
    – Richard Hardy
    Commented Apr 13, 2020 at 8:11
  • $\begingroup$ on the image file if you add some whitespace it will shrink and fit to width. Alternatively, you may use a lower resolution image. $\endgroup$
    – Always Confused
    Commented Jul 23, 2020 at 17:46
  • $\begingroup$ Use ImageMagick. E.g., convert xxx -density 600 -resize 25% xxx. $\endgroup$
    – chl
    Commented Nov 27, 2020 at 20:02
  • $\begingroup$ @chl, thanks. I was looking for a built-in solution. Otherwise there are multiple services to choose from. I use FastStone Photo Resizer every now and then. $\endgroup$
    – Richard Hardy
    Commented Nov 27, 2020 at 20:58
  • $\begingroup$ No built-in skrinking feature, AFAIK. +1, BTW, this was a very nice free update from the authors of this memorable textbook. $\endgroup$
    – chl
    Commented Nov 27, 2020 at 21:22
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It's not a textbook but Bayesian Methods in the Search for the MH370 is a great introduction to particle filters.

S. Davey, N. Gordon, I. Holland, M. Rutten, and J. Williams, Bayesian Methods in the Search for MH370 (2016)

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A digital textbook on probability and statistics by M. Taboga can be found at https://www.statlect.com The level is intermediate. It has hundreds of solved exercises and examples, as well as step-by-step proofs of all the results presented.

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For an introduction to the statistical analysis of networks, Statistical Analysis of Networks by Konstantin Avrachenkov and Maximilien Dreveton. The paper version isn't free, but the PDF version is. It is published under a Creative Commons By-NC licence.

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