- Location-scale family
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 parameterμ and a scale parameterσ ≥ 0; if "X" is any random variablewhose probability distribution belongs to such a family, then "Y" = μ + σ"X" is another, and every distribution in the family is of that form.
In other words, a class Ω of probability distributions is a location-scale family if whenever "F" is the
cumulative distribution functionof a member of Ω and μ is any real number and σ > 0, then "G"("x") = "F"(μ + σ"x") is also the cumulative distribution function of a member of Ω.
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