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Statistical Model

A statistical model may be a mathematical model which embodies a group of assumptions of statistics concerning the generation of sample data (and similar data from a bigger population). A model of statistics represents, often in idealized form, the data-generating process.

A statistical model is typically 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".

All statistical hypothesis tests and every one statistical estimators are derived via statistical models. More generally, statistical models are a part of the inspiration of statistical inference.

A statistical model may be a special class of mathematical model. What distinguishes a statistical model from other mathematical models is that a statistical model is non-deterministic. Thus, during a statistical model specified through equations of mathematics equations, a number of the variables don't have specific values, but instead have probability distributions; i.e. some of the variables are stochastic. In the above example with children's heights, ε may be a random variable; without that stochastic variable, the model would be deterministic.

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