In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution.

A statistic can be used to estimate a scale parameter so long as it:

Is location-invariant,

Scales linearly with the scale parameter, and

Converges as the sample size grows.

Various measures of statistical dispersion satisfy these. In order to make the statistic a consistent estimator for the scale parameter, one must in general multiply the statistic by a constant scale factor. This scale factor is defined as the theoretical value of the value obtained by dividing the required scale parameter by the asymptotic value of the statistic. Note that the scale factor depends on the distribution in question.