By contrast, packages like SPSS, Systat, SAS, Gauss, JMP, R and S-Plus provide a numerical / graphical toolset. They can illustrate, they can simulate, and they can find approximate numerical solutions to numerical problems, but they generally cannot find exact symbolic solutions to statistical problems.

Features include: a complete suite for manipulating arbitrary pdf's univariate and multivariate automated expectations, probability, plotting automated transformations (functions of random variables) products of random variables Maximum / Minimum of random variables generating functions inversion theorems symbolic maximum likelihood estimation numerical maximum likelihood estimation automated Pearson curve fitting Johnson curve fitting Gram-Charlier expansions non-parametric kernel density estimation moment conversion formulae component-mix and parameter-mix distributions stable distributions copulae random number generation asymptotics decision theory order statistics order statistics for non-identical distributions Fisher Information h-statistics, k-statistics, polykays checking and correction of textbook formulae and more

Advanced user interface
The new mathStatica 2.72 makes full use of the latest interface technologies in Mathematica. Palettes provide easy access to hundreds of distributions. Fancy on-line HELP is fully integrated into the new Mathematica Help system. And, mathStatica 2.7 is perfectly integrated with the included e-text Mathematical Statistics with Mathematica, so that every example is live, every equation is at the reader’s finger tips, every diagram can be generated on the fly, equations are hyperlinked, footnotes pop-up, cross-references are live, the index is hyperlinked, and animations are real-time interactive.

Hundreds of Worked Examples
mathStatica seamlessly integrates with the included e-text

providing hundreds of live worked examples on a remarkable variety of topics - see the Book Index.

Award Winning Software
mathStatica has won multiple international awards at major conferences in the USA and Europe.

mathStatica is now used in over 57 countries, at almost every major university in the USA, and at institutions such as Boeing, Google, NASA, Los Alamos Labs, the Federal Drug Administration, the Max Planck Institute, ..., and at financial institutions such as Bank of America, Deutsche Bank, the US Federal Reserve, HBOS, KPMG, Reuters, the SEC, Standard Chartered, UBS etc.

Delightfully Simple
By delightfully simple, we mean both (i) easy to use, and (ii) able to solve problems that seem difficult, but which are formally quite simple. Consider, for instance, playing a devilish game of chess against a strong chess computer: in the middle of the game, after a short pause, the computer announces, “Mate in 16 moves”. The problem it has solved might seem fantastically difficult, but it is really just a 'delightfully simple' finite problem that is conceptually no different than looking just two moves ahead. The salient point is that as soon as one has a tool for solving such problems, the notion of what is difficult changes completely.

For Mathematica
mathStatica is built on top of the industrial strength backbone of Mathematica. It takes full advantage of Mathematica’s superb symbolic, numerical and graphical engine, as well as its sophisticated notebook user interface, to create the leading application package for solving problems in mathematical statistics.

Arbitrary precision numerics
Whereas most software packages provide only finite-precision numerics, Mathematica also provides an arbitrary-precision numerical engine: if accuracy is important, Mathematica excels. As McCullough notes:

“ By virtue of its variable precision arithmetic and symbolic power, Mathematica’s performance on these reliability tests far exceeds any finite-precision statistical package.”
Computational Statistics, 15 (p.296)

Check that textbook solution!
In the process of developing and testing mathStatica, its output has been compared with thousands of known textbook solutions. When disparities are found, numerical or other methods can usually be used to check who is wrong. In this manner, the authors have encountered many errors in highly respected reference texts in mathematical statistics. Some of these textbook errors are now listed at our new Spot the Error page. Sometimes these are just 'typos', and sometimes the known solution is just fundamentally wrong. If you are passionate about accuracy, then mathStatica is a superb tool to assist in checking both your own work and the work of others.