Definition
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.
Read more about this topic: Scale Parameter
Famous quotes containing the word definition:
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)