Note
Power law distributions have a well defined mean only if the exponent exceeds 1 and have a finite variance only when the exponent exceeds two. To apply the central limit theorem (and related statistics) to a power law distributed variable it is first necessary to ensure that the distribution has an exponent that exceeds 2.
Read more about this topic: Power Law
Famous quotes containing the word note:
“During the cattle drives, Texas cowboy music came into national significance. Its practical purpose is well known—it was used primarily to keep the herds quiet at night, for often a ballad sung loudly and continuously enough might prevent a stampede. However, the cowboy also sang because he liked to sing.... In this music of the range and trail is “the grayness of the prairies, the mournful minor note of a Texas norther, and a rhythm that fits the gait of the cowboy’s pony.””
—Administration in the State of Texa, U.S. public relief program (1935-1943)
“And songs climb out of the flames of the near campfires,
Pale, pastel things exquisite in their frailness
With a note or two to indicate it isn’t lost,
On them at least. The songs decorate our notion of the world
And mark its limits, like a frieze of soap-bubbles.”
—John Ashbery (b. 1927)
“There is a note in the front of the volume saying that no public reading ... may be given without first getting the author’s permission. It ought to be made much more difficult to do than that.”
—Robert Benchley (1889–1945)