Estimation of Parameters
A series of N measurements drawn from a von Mises distribution may be used to estimate certain parameters of the distribution. (Borradaile, 2003) The average of the series is defined as
and its expectation value will be just the first moment:
In other words, is an unbiased estimator of the first moment. If we assume that the mean lies in the interval, then Arg will be a (biased) estimator of the mean .
Viewing the as a set of vectors in the complex plane, the statistic is the square of the length of the averaged vector:
and its expectation value is:
In other words, the statistic
will be an unbiased estimator of and solving the equation for will yield a (biased) estimator of . In analogy to the linear case, the solution to the equation will yield the maximum likelihood estimate of and both will be equal in the limit of large N.
Read more about this topic: Von Mises Distribution
Famous quotes containing the words estimation and/or parameters:
“A higher class, in the estimation and love of this city- building, market-going race of mankind, are the poets, who, from the intellectual kingdom, feed the thought and imagination with ideas and pictures which raise men out of the world of corn and money, and console them for the short-comings of the day, and the meanness of labor and traffic.”
—Ralph Waldo Emerson (1803–1882)
“What our children have to fear is not the cars on the highways of tomorrow but our own pleasure in calculating the most elegant parameters of their deaths.”
—J.G. (James Graham)