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A three-parameter generalized von Mises distribution

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  • Sungsu Kim
  • Ashis SenGupta

Abstract

In this paper, we propose a three-parameter generalized von Mises distribution, called the asymmetric generalized von Mises (AGvM) distribution, which is an extension of the von Mises (vM) distribution, and a subclass of the generalized von Mises (GvM) distribution introduced by Gatto and Jammalamadaka (Stat Methodol 4:341–353, 2007 ). The three parameter model belongs to an exponential family of distributions and can be used to model both asymmetric and bimodal data. Some properties are studied and interpretation of the parameters is discussed in detail. It is shown that the parameters of the AGvM distribution are particularly easy to interpret and contain a skewness measure as one of its three parameters. A real environmental data set example is provided to illustrate the goodness of fit for AGvM distribution. Copyright Springer-Verlag 2013

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  • Sungsu Kim & Ashis SenGupta, 2013. "A three-parameter generalized von Mises distribution," Statistical Papers, Springer, vol. 54(3), pages 685-693, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:685-693
    DOI: 10.1007/s00362-012-0454-1
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    Cited by:

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    2. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    3. Xiaoping Zhan & Tiefeng Ma & Shuangzhe Liu & Kunio Shimizu, 2019. "On circular correlation for data on the torus," Statistical Papers, Springer, vol. 60(6), pages 1827-1847, December.
    4. Mojtaba Hatami & Mohammad Hossein Alamatsaz, 2019. "Skew-symmetric circular distributions and their structural properties," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 953-969, December.
    5. Xiaoping Zhan & Tiefeng Ma & Shuangzhe Liu & Kunio Shimizu, 2018. "Markov-Switching Linked Autoregressive Model for Non-continuous Wind Direction Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 410-425, September.
    6. Arnab Kumar Laha & A. C. Pravida Raja & K. C. Mahesh, 2019. "SB-robust estimation of mean direction for some new circular distributions," Statistical Papers, Springer, vol. 60(3), pages 877-902, June.

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