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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.

If a family of probability distributions is such that there is a parameter *s* (and other parameters *θ*) for which the cumulative distribution function satisfies

then *s* is called a **scale parameter**, since its value determines the "scale" or statistical dispersion of the probability distribution. If *s* is large, then the distribution will be more spread out; if *s* is small then it will be more concentrated.

If the probability density exists for all values of the complete parameter set, then the density (as a function of the scale parameter only) satisfies

where *f* is the density of a standardized version of the density.

An estimator of a scale parameter is called an **estimator of scale.**

We can write in terms of , as follows:

Because *f* is a probability density function, it integrates to unity:

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Scale_parameter

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