Suppose that we have an [[indexed family]] of distributions. If the index is also a parameter of the members of the family, then the family is a [[parameterized family]]. Among [[parametric family|parameterized families]] of distributions are the [[normal distribution]]s, the [[Poisson distribution]]s, the [[binomial distribution]]s, and the [[exponential family|exponential family of distributions]]. For example, the family of [[normal distribution]]s has two parameters, the [[mean]] and the [[variance]]: if those are specified, the distribution is known exactly. The family of [[chi-squared distribution]]s can be indexed by the number of [[degrees of freedom (statistics)|degrees of freedom]]: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized.
