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Statistics Packages
(SAS, SPSS, S-PLUS, R, Stata, JMP, Minitab, SYSTAT, UNISTAT, STATISTICA, ...)
Widely used for more than a decade as a high-powered statistical system, Mathematica's capabilities in statistics-related areas have steadily grown. Mathematica includes industrial-strength versions of the usual statistics and visualization capabilities, together with many important unique capabilities, made possible by its broad overall scope and extensibility, immense interconnected web of algorithms and integrated programming language and interface framework.
Mathematica dramatically raises the bar for statistical computation—making possible a vastly higher level of integration of the complete analysis workflow, as well as providing major extensibility beyond the specific functions implemented in particular statistical systems.
Mathematica uses its unique core architecture to provide convenient import of the world's broadest range of data formats. Then, Mathematica's well-developed symbolic language makes it easy to specify arbitrarily extensible statistical models and data analysis methods. With its unique approach to computational aesthetics, Mathematica automates the generation of compelling visualizations—and allows any output or computation to immediately become interactive and dynamic.
An important feature of Mathematica is its integrated notebook mechanism, in which a single document can store a complete, formatted, editable, executable history of an analysis, complete with live graphics, interactive controls and arbitrary typeset tabular, mathematical and other material. Mathematica allows notebooks to be built up interactively, or generated programmatically, then immediately exported in a wide range of online, print and web formats.
Most existing statistical packages have gradually evolved from specific libraries of functions. Mathematica's broader overall conception, vastly greater range of capabilities and integration with the latest computing technologies allows it easily to incorporate the latest developments in statistics and data analysis that would be difficult or impossible for narrowly defined statistics systems.
Typical Statistics Package Features in Mathematica:
- Data import and export to over 100 formats »
- Highly developed 2D and 3D data visualization capabilities
- Standard statistical functions for data and distributions »
- Symbolic and numerical statistical distributions »
- Efficient random number generation for all distributions »
- General constrained nonlinear fitting »
- Built-in exploratory data analysis, cluster analysis, etc. »
- Efficient built-in string and text analysis »
- Built-in unified array-oriented, fully extensible language »
- Ability to export complete reports in PDF, HTML, TEX, etc. »
- Full cross-platform system support
- Multiple textbooks cover statistics in Mathematica
- 20-year history of leading-edge algorithm development »
Key Advantages of Mathematica for Statistics:
- Support for gigabyte-sized datasets »
- Built-in industrial-strength linear algebra and optimization »
- Full coverage of mathematical special functions »
- Symbolic statistics, giving formulas as results
- Full integration of broad computational capabilities
- Integrated input and output of traditional mathematical notation
- Immediate creation of interactive interfaces for all computations »
- Built-in fully programmable dynamic formatted document generation »
- Ability to extract data from web pages, documents and many specialized formats »
- Built-in curated data sources for scientific, socioeconomic, financial, etc. data »
- Built-in automated typeset table layout »
- Computational aesthetics automation of all aspects of visualization
- Full multiparadigm programming language for data manipulation
- Full programmable extensibility for adding arbitrary functionality
- Capability for symbolic specification of statistical models »
- Seamless support for exact- and arbitrary-precision computation »
- Uniform high-quality language, with full professional development tools »
- Deployment with webMathematica
- Broad statistics coverage in The Wolfram Demonstrations Project
- Integration with statistics information in Wolfram MathWorld
Interoperability with Statistics Packages:
- Built-in connectivity for all standard database systems »
- Full import and export to spreadsheets and other standard data formats »
- Import and export of CSV, TSV, XLS, XPORT, MTP, etc. »
- Full APIs for C, C++, C#, Java, etc. »
Interesting Tidbits:
- Mathematica's highly efficient random generator is based on NKS methods
- A study in 2000 found Mathematica unique in giving accurate results for statistical functions
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