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 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)
“My note to you I certainly did not expect to see in print; yet I have not been much shocked by the newspaper comments upon it. Those comments constitute a fair specimen of what has occurred to me through life. I have endured a great deal of ridicule without much malice; and have received a great deal of kindness, not quite free from ridicule. I am used to it.”
—Abraham Lincoln (1809–1865)