Group family

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.[1]

Consideration of a particular family of distributions as a group family can, in statistical theory, lead to the identification of an ancillary statistic.[2]

References

  1. ↑ Lehmann, E. L.; George Casella (1998). Theory of Point Estimation (2nd ed.). Springer. ISBN 0-387-98502-6.
  2. ↑ Cox, D.R. (2006) Principles of Statistical Inference, CUP. ISBN 0-521-68567-2 (Section 4.4.2)
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