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:
“For sounds in winter nights, and often in winter days, I heard the forlorn but melodious note of a hooting owl indefinitely far; such a sound as the frozen earth would yield if struck with a suitable plectrum, the very lingua vernacula of Walden Wood, and quite familiar to me at last, though I never saw the bird while it was making it.”
—Henry David Thoreau (1817–1862)
“What says the Clock in the Great Clock Tower?
And all alone comes riding there
The King that could make his people stare,
Because he had feathers instead of hair.
A slow low note and an iron bell.”
—William Butler Yeats (1865–1939)
“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)