Statistical Parameter must not be confound with a population parameter
A parameter is a numerical characteristic, feature, or measurable factor that help in defining a particular model.
Unlike variables, parameters are not listed among the arguments that the function takes.
When parameters are present in a function, the function definition defines a whole family of functions, one for every valid set of values of the parameters.
Usually a model is designed to explain the relationships that exist among quantities which can be measured, these are the variables of the model. To formulate these relationships, “constants” are introduced which stand for inherent properties of nature. These are the parameters.
For instance, one could define a general quadratic function by defining:
<math>
f(x)=ax^{n}+bx+c
</math>
where:
Parametrized objects (families of) depends on a set of parameters:
Examples:
Among parameterized families of distributions are: