Moments
The raw vector (or trigonometric) moments of a circular distribution are defined as
where is any interval of length and is the PDF of the circular distribution. Since the integral is unity, and the integration interval is finite, it follows that the moments of any circular distribution are always finite and well defined.
Sample moments are analogously defined:
The population resultant vector, length, and mean angle are defined in analogy with the corresponding sample parameters.
In addition, the lengths of the higher moments are defined as:
while the angular parts of the higher moments are just . The lengths of the higher moments will all lie between 0 and 1.
Read more about this topic: Directional Statistics
Famous quotes containing the word moments:
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saying blackberry, blackberry, blackberry.”
—Robert Hass (b. 1941)
“As the tragic writer rids us of what is petty and ignoble in our nature, so also the humorist rids us of what is cautious, calculating, and priggishabout half of our social conscience, indeed. Both of them permit us, in blessed moments of revelation, to soar above the common level of our lives.”
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—Havelock Ellis (18591939)