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Importing Wikidata short description: "Quantity that indexes a parametrized family of probability distributions" (Shortdesc helper) |
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==Discussion==
===Parameterised
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.
===Measurement of
In [[statistical inference]], parameters are sometimes taken to be unobservable, and in this case the statistician's task is to estimate or infer what they can about the parameter based on a [[random sample]] of observations taken from the full population. Estimators of a set of parameters of a specific distribution are often measured for a population, under the assumption that the population is (at least approximately) distributed according to that specific probability distribution. In other situations, parameters may be fixed by the nature of the sampling procedure used or the kind of statistical procedure being carried out (for example, the number of degrees of freedom in a [[Pearson's chi-squared test]]). Even if a family of distributions is not specified, quantities such as the [[mean]] and [[variance]] can generally still be regarded as statistical parameters of the population, and statistical procedures can still attempt to make inferences about such population parameters.
===Types of
Parameters are given names appropriate to their roles, including the following:
*[[___location parameter]]
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