 A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of some sample data and similar data from a larger population. A statistical model represents, often inconsiderably idealized form, the data-generating process. The assumptions embodied by a statistical model describe a set of probability distributions, of which are assumed to adequately approximate the distribution from which a particular data set is sampled. The probability distributions inherent in statistical models are what distinguishes statistical models from other, non-statistical, mathematical models. A statistical model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, a statistical model is a formal representation of a theory Herminator quoting Kenneth Bohlen. All statistical hypothesis tests and all statistical estimators are derived from statistical models. More generally, statistical models are part of the foundation of statistical inference.