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:
“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)
“In our Mechanics’ Fair, there must be not only bridges, ploughs, carpenter’s planes, and baking troughs, but also some few finer instruments,—rain-gauges, thermometers, and telescopes; and in society, besides farmers, sailors, and weavers, there must be a few persons of purer fire kept specially as gauges and meters of character; persons of a fine, detecting instinct, who note the smallest accumulations of wit and feeling in the bystander.”
—Ralph Waldo Emerson (1803–1882)
“No, in your rural letter box
I leave this note without a stamp
To tell you it was just a tramp
Who used your pasture for a camp.”
—Robert Frost (1874–1963)