Abstract
Motivated by the success of the Box and Cox (J R Stat Soc Ser B Stat Methodol 26:211–243, 1964) [2] transformation to near normality, we consider the transformation of directional data to an approximate von Mises distribution. Variation about the central value of this von Mises distribution is symmetric and a single shape parameter controls the amount. The circular nature of directions requires the development of some novel transformations that are completely unrelated to transformations of the positive real line. We introduce a class of transformations indexed by two parameters. We verify the improvement of a von Mises approximation for three data sets that are well known to exhibit asymmetry. Then, we discuss the computational difficulties and give a proof of the consistency and asymptotic normality of the maximum likelihood estimators of all parameters.
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Acknowledgements
The author expresses his sincere appreciation to Dr. Steve Verrill, United States Forest Products Laboratory, for his excellent help in fitting the four-parameter models for the three examples that appear in this paper.
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Johnson, R.A. (2022). Transformations to Improve the Approximation by a von Mises Distribution. In: SenGupta, A., Arnold, B.C. (eds) Directional Statistics for Innovative Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1044-9_8
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DOI: https://doi.org/10.1007/978-981-19-1044-9_8
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