- Location-scale family
In

probability theory , especially as that field is used instatistics , a**location-scale family**is a family ofunivariate probability distribution s parametrized by alocation parameter μ and ascale parameter σ ≥ 0; if "X" is anyrandom variable whose 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 function of 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.**Examples***

normal distribution

*Cauchy distribution

*uniform distribution

*logistic distribution **References**http://www.ds.unifi.it/VL/VL_EN/special/special1.html

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