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The circular mean is one of the simplest examples of directional statistics and of statistics of non-Euclidean spaces. This computation produces a different result than the arithmetic mean, with the difference being greater when the angles are widely distributed.
There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, a form of the standard deviation. Another is the R95, which is the radius of the circle where 95% of the values would fall, a 95% confidence interval .
Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, R n), axes (lines through the origin in R n) or rotations in R n.
A circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic , lexicographic and linguistic .
The mean of a set of observations is the arithmetic average of the values; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or the most likely value (mode). For example, mean income is typically skewed upwards by a small number of people with very large incomes, so that the majority have an ...
The von Mises distribution is the maximum entropy distribution for circular data when the real and imaginary parts of the first circular moment are specified. The von Mises distribution is a special case of the von Mises–Fisher distribution on the N -dimensional sphere.
In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2π). [1] A circular distribution is often a continuous probability distribution , and hence has a probability density , but such distributions can also be ...
Thus, we define circular moments by placing all measured angles on a unit circle, then calculating the moments of these points. The Yamartino method, introduced by Robert J. Yamartino in 1984, solves both problems [ 2 ] A further discussion of the Yamartino method, along with other methods of estimating the standard deviation of wind direction ...