Location-scale family

In probability theory, especially as that field is used in statistics, a location-scale family is a family of univariate probability distributions parametrized by a location parameter &mu; and a scale parameter &sigma; &ge; 0; if X is any random variable whose probability distribution belongs to such a family, then Y = &mu; + &sigma;X is another, and every distribution in the family is of that form.

In other words, a class &Omega; of probability distributions is a location-scale family if whenever F is the cumulative distribution function of a member of &Omega; and &mu; is any real number and &sigma; > 0, then G(x) = F(&mu; + &sigma;x) is also the cumulative distribution function of a member of &Omega;.

Examples

 * normal distribution
 * Cauchy distribution
 * uniform distribution