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http://dx.doi.org/10.5351/KJAS.2010.23.6.1125

A Projected Exponential Family for Modeling Semicircular Data  

Kim, Hyoung-Moon (Department of Applied Statistics, Konkuk University)
Publication Information
The Korean Journal of Applied Statistics / v.23, no.6, 2010 , pp. 1125-1145 More about this Journal
Abstract
For modeling(skewed) semicircular data, we derive a new exponential family of distributions. We extend it to the l-axial exponential family of distributions by a projection for modeling any arc of arbitrary length. It is straightforward to generate samples from the l-axial exponential family of distributions. Asymptotic result reveals that the linear exponential family of distributions can be used to approximate the l-axial exponential family of distributions. Some trigonometric moments are also derived in closed forms. The maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for a goodness of t test of the l-axial exponential family of distributions. Samples of orientations are used to demonstrate the proposed model.
Keywords
Uniformly minimum variance unbiased estimator; maximum likelihood estimator; skewed l-axial data; Kolmogorov-Smirnov test; delta method;
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Times Cited By KSCI : 1  (Citation Analysis)
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