location-scale family of distributions

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For any distribution function f(x), a family of distribution functions, indexed by the parameters μ (the location parameter) and σ (the scale parameter), of the form (1/σ)f(xμ)/σ). An example is the normal family: a normal distribution with mean μ and variance σ2 can be obtained from the standard normal distribution by stretching (σ > 1) or contracting (σ < 1) the graph of standard normal probability density function with the scale parameter and then shifting the graph by the location parameter, so that the point that was above 0 is now above μ.

Subjects: Economics.

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