Estimation of Parameters
A series of N measurements zn = e iθn drawn from a wrapped normal distribution may be used to estimate certain parameters of the distribution. The average of the series z is defined as
and its expectation value will be just the first moment:
In other words, z is an unbiased estimator of the first moment. If we assume that the mean μ lies in the interval [−π, π), then Arg z will be a (biased) estimator of the mean μ.
Viewing the zn as a set of vectors in the complex plane, the R2 statistic is the square of the length of the averaged vector:
and its expected value is:
In other words, the statistic
will be an unbiased estimator of e−σ2, and ln(1/Re2) will be a (biased) estimator of σ2
Read more about this topic: Wrapped Normal Distribution
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