Statistical Models

Def Statistical Model (Family)
A statistical model (family) is a collection of probability distributions on some sample space. We assume that the collection, , is indexed by some set . The set is called the parameter space. For each , let denote the corresponding member of the collection. Then a statistical model can be written as .

Def Parametric Model (Family)
A statistical model (family) is parametric if for some positive integer .

Probability Distributions

The Basic Distributions

Uniform Distribution

The Exponential Family

• Binomial Distribution
• Beta Distribution
• Gamma Distribution
• Pareto Distribution
• Exponential Distribution
• Poisson Distribution