In probability theory, especially as that field is used in statistics, a group family of probability distributions is a family obtained by subjecting a random variable with a fixed distribution to a suitable family of transformations such as a location-scale family, or otherwise a family of probability distributions acted upon by a group.
Consideration of a particular family of distributions as a group family can, in statistical theory, lead to the identification of an ancillary statistic.
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Group family Wikipedia(Text) CC BY-SA