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The semi-circular normal distribution. (English) Zbl 1133.62307

Summary: We introduce the semicircular normal (SCN) family of distributions for observations on the half-circle and for axial data. Suitably transformed, it can also be used for fully circular data. For small angles, the SCN and the normal distribution are equivalent and there is a limiting relationship between the SCN and the von Mises distribution. We also develop a bivariate version of the SCN. Inference for the SCN is straightforward, using the method of moments, maximum likelihood, or Bayesian estimators. We illustrate the applicability of the SCN with some examples.

MSC:

62E10 Characterization and structure theory of statistical distributions
62H11 Directional data; spatial statistics
62F10 Point estimation
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