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)
“The most considerable difference I note among men is not in their readiness to fall into error, but in their readiness to acknowledge these inevitable lapses.”
—Thomas Henry Huxley (1825–95)
“The finch, the sparrow, and the lark,
The plainsong cuckoo grey,
Whose note full many a man doth mark
And dares not answer nay.”
—William Shakespeare (1564–1616)