Examples
In general, any random variable X is a member of a location-scale family with an infinite number of members; each of these members Y is distributed the same as a + bX for real numbers a and b > 0. However, the form of the distribution function for a + bX, and hence for Y, may differ from the form of the distribution function for X. Well-known families in which the functional form of the distribution is retained throughout the family include the following:
- Normal distribution
- Elliptical distribution
- Cauchy distribution
- Uniform distribution (continuous)
- Uniform distribution (discrete)
- Logistic distribution
- Laplace distribution
- Student's t-distribution
- Generalized extreme value distribution
Read more about this topic: Location-scale Family
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