Statistical Computing Languages. These are high-level programming languages that are well-suited for statistical computing.

• C/C++. Effective if used in combination with a good numerical/statistical library such as the GNU Scientific Library (GSL).
• Fortran. Particularly Fortran 90 and later. Free subroutines/functions, libraries, and modules can be found at Statlib, Netlib, and on Alan Miller's Fortran Software website.
• GAUSS. A student version (GAUSS Light) is available for a very nominal fee. The student version is restricted in terms of the number of elements in a given array (although one can get around this problem some of the time with clever programming). GAUSS is available for Unix/Linux and Windows platforms. Several libraries are available for GAUSS although, unfortunately, discounted student versions are not available. They will, however, work with the student version of GAUSS.
• Ox (Objected-Oriented Matrix Language) . Ox is an object-oriented matrix language with a comprehensive mathematical and statistical function library. Matrices can be used directly in expressions, for example to multiply two matrices, or to invert a matrix. Use of the object oriented features is optional, but facilitates code re-use. The syntax of Ox is similar to the C, C++ and Java languages. This similarity is most clear in syntax items such as loops, functions, arrays and classes. Ox is one of the fastest of the higher high-level statistical computing languages. The console version of Ox may be used free of charge for academic and research purposes. Binary distributions are available for Unix/Linux and Windows platforms. Some add-on packages are also available.
• PDL (Perl Data Language) . A Perl extension package. The PDL concept is to give standard perl5 the ability to compactly store and speedely manipulate the large N-dimensional data sets which are the bread and butter of scientific computing. It may be used in Perl scripts or within an interactive shell (perldl).
• R . R is `GNU S' - A language and environment for statistical computing and graphics. R is similar to the award-winning S system, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, ...). R is designed as a true computer language with control-flow constructions for iteration and alternation, and it allows users to add additional functionality by defining new functions. For computationally intensive tasks, C, C++ and Fortran code can be linked and called at run time . R is freely available under the terms of the Free Software Foundation's GNU General Public License. Binary distributions are available for Unix/Linux, Windows, and MacOS platforms. R is similar, syntactically, to S and S-PLUS although there are some important differences (see the FAQ for more information). A variety of add-on packages are available for R, including many of those available for S-PLUS and some that are not.
• XLISP-STAT . Lisp-stat is an extensible statistical computing environment for data analysis, statistical instruction and research, with an emphasis on providing a framework for exploring the use of dynamic graphical methods. Extensibility is achieved by basing Lisp-Stat on the Lisp language, in particular on a subset of Common Lisp. Lisp-Stat extends standard Lisp arithmetic operations to perform element-wise operations on lists and vectors, and adds a variety of basic statistical and linear algebra functions. A portable window system interface forms the basis of a dynamic graphics system that is designed to work identically in a number of different graphical user interface environments, such as the Macintosh operating system, the X window system, and Microsoft Windows. A prototype-based object-oriented programming system is used to implement the graphics system and to allow it to be customized and adapted. The object-oriented programming system is also used as the basis for statistical model representations, such as linear and nonlinear regression models and generalized linear models. Many aspects of the system design were motivated by the S language. XLISP-STAT is a version of Lisp-Stat based on the XLISP language. Binary distributions for Unix/Linux, MacOS, and Windows platforms are freely available

• BUGS. Bayesian inference Using Gibbs Sampling is a piece of computer software for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. It grew from a statistical research project at the MRC Biostatistics Unit, but now is developed jointly with the Imperial College School of Medicine at St Mary's, London. Free binaries of classic BUGS (i.e., text/batch-file based) are available for a variety of platforms including Unix, Linux, and MSDOS. WinBUGS is a GUI version for Windows.
  
• LEM. General program for the analysis of categorical data using a wide variety of models (e.g., log-linear, association, regression, path, latent structure, and event history). Estimation is via maximum likelihood with an EM algorithm where necessary. Free binaries are available for Windows and DOS only. 
• MIXOR/MIXNO/MIXREG/MIXPREG . [A suite of programs for fitting mixed-effects models] including mixed-effects linear regression, mixed-effects logistic regression for nominal or ordinal outcomes, mixed-effects probit regression for ordinal outcomes, mixed-effects Poisson regression, and mixed-effects grouped-time survival analysis.These models are also called multilevel models, hierarchical linear models, random-effects models, and random coefficients models, to name a few. Estimation is based on maximum likelihood with numerical integration. Free binaries are available for Windows and DOS only. 
• Mx. Mx is a combination of a matrix algebra interpreter and a numerical optimizer. It enables exploration of matrix algebra through a variety of operations and functions. There are many built-in fit fuctions to enable structural equation modeling and other types of statistical modeling of data. It offers the fitting fuctions found in commercial software such as LISREL, LISCOMP, EQS and CALIS, along with facilities for maximum likelihood estimation of parameters from missing data structures, under normal theory. Complex 'nonstandard' models are easy to specify. For further general applicability, it allows the user to define their own fit functions, and optimization may be performed subject to linear and nonlinear equality or boundary constraints. Mx is well-suited for modeling quite general mean and covariance structure models. Free binaries are available for Windows and Unix/Linux. The Windows version features a GUI interface.

• GGobi. GGobi is a data visualization system for viewing high-dimensional data and is the next edition of xgobi. It provides a new interface to many of the features of xgobi, built using Gtk, the GIMP toolkit and provides several new features. Free and open source. Source for Unix/Linux is available as well as a Windows binary.
• Gnuplot. Gnuplot is a portable command-line driven interactive data and function plotting utility for UNIX, IBM OS/2, MS Windows, DOS, Macintosh, VMS, Atari and many other platforms. The software is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally intended as to allow scientists and students to visualize mathematical functions and data. It does this job pretty well, but has grown to support many non-interactive uses, including web scripting and integration as a plotting engine for third-party applications like Octave. Gnuplot has been supported and under development since 1986. Gnuplot supports many types of plots in either 2D and 3D. It can draw using lines, points, boxes, contours, vector fields, surfaces, and various associated text. It also supports various specialized plot types. Gnuplot supports many different types of terminals: interactive screen terminals (with mouse and hotkey functionality), pen plotters (like hpgl), printers (including postscript and many color devices), and printings to output file as vectorial pseudo-devices like LaTeX, metafont, pdf, svg, or bitmap png. Gnuplot is easily extensible to include new devices.

• Mathomatic is a small, portable, general purpose CAS (Computer Algebra System) written entirely in C. It is totally free software (GNU LGPL license). This is a console mode application that compiles and runs under any operating system with a C compiler.
  
• Maxima is a full symbolic computation program. It is full featured doing symbolic manipulation of polynomials, matrices, rational functions, integration, Todd-coxeter, graphing, bigfloats. It has a symbolic debugger source level debugger for maxima code. Maxima is based on the original Macsyma developed at MIT in the 1970's. Maxima is distributed under the GNU General Public License. Windows and linux binaries are available. Nice interfaces to Maxima are available via (X)Emacs and TeXmacs.
  

• MiKTeX . A very complete distribution of TeX/LaTeX for Windows. This is almost everything you would ever need. A good front-end for MiKTeX is WinEdt (see below).
• Kile. A TeX/LaTeX editor and interface.
• LyX . A word processor that uses LaTeX in the background. It is also able to import and export LaTeX files. Functionally, it is not unlike EXP. LyX is available for Unix/Linux platforms.
• TeXmacs. GNU TeXmacs is a free scientific text editor, which was both inspired by TeX and GNU Emacs. The editor allows you to write structured documents via a wysiwyg (what-you-see-is-what-you-get) and user friendly interface. New styles may be created by the user. The program implements high-quality typesetting algorithms and TeX fonts, which help you to produce professionally looking documents. The high typesetting quality still goes through for automatically generated formulas, which makes TeXmacs suitable as an interface for computer algebra systems. TeXmacs also supports the Guile/Scheme extension language, so that you may customize the interface and write your own extensions to the editor. Converters exist for TeX/LaTeX and they are under development for Html/MathML/Xml. In the future, TeXmacs is planned to evolve towards a complete scientific office suite, with spreadsheet capacities, a technical drawing editor and a presentation mode. Binaries are available for Linux, Unix, Windows, and Mac.
  
• WinEdt . A Win32 text editor that works very well as a front-end for MiKTeX. It is shareware but a single-user license is inexpensive. WinEdt should not be confused with WinEdit which is an entirely different program.