Location–scale family
In probability theory, especially in mathematical statistics, a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random variable X {\displaystyle X} whose probability distribution function belongs to such a family, the distribution function of Y = d a + b X {\displaystyle Y\,{\stackrel {d}{=}}\,a+bX} also belongs to the family (where = d {\displaystyle {\stackrel {d}{=}}} means "equal in distribution"—that is, "has the same distribution as").