Guardiola, José H.; Stamey, James D.; Seaman, John W.; Elsalloukh, Hassan The semi-circular normal distribution. (English) Zbl 1133.62307 Far East J. Theor. Stat. 20, No. 2, 207-216 (2006). 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 Keywords:axial data; semicircular distribution; von Mises distribution for half-circle; angular distribution PDFBibTeX XMLCite \textit{J. H. Guardiola} et al., Far East J. Theor. Stat. 20, No. 2, 207--216 (2006; Zbl 1133.62307)