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)
“Alexander Woollcott broadcasts the story of the wife who returned a dog to the Seeing Eye with this note attached: “I am sending the dog back. My husband used to depend on me. Now he is independent, and I never know where he is.””
—For the State of New Jersey, U.S. public relief program (1935-1943)
“The note of the white-throated sparrow, a very inspiriting but almost wiry sound, was first heard in the morning, and with this all the woods rang. This was the prevailing bird in the northern part of Maine. The forest generally was alive with them at this season, and they were proportionally numerous and musical about Bangor. They evidently breed in that State.”
—Henry David Thoreau (1817–1862)