# Statistical model

## Type of mathematical model / From Wikipedia, the free encyclopedia

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A **statistical model** is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.^{[1]} When referring specifically to probabilities, the corresponding term is **probabilistic model**. All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman Adèr quoting Kenneth Bollen).^{[2]}