Far East Journal of Theoretical Statistics
Volume 20, Issue 2, Pages 207 - 216
(November 2006)
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THE SEMI-CIRCULAR NORMAL DISTRIBUTION
José H. Guardiola (U. S. A.), James D. Stamey (U. S. A.), John W. Seaman (U. S. A.) and Hassan Elsalloukh (U. S. A.)
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Abstract: 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
method of moments, maximum likelihood, or Bayesian estimators. We illustrate the
applicability of the SCN with some examples. |
Keywords and phrases: axial data, semicircular distribution, von Mises distribution
for half-circle, angular distribution. |
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